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MacBinary | 1996-03-31 | 163.6 KB | [ SNKR/KRAK]
open in: MacOS 8.1
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Win98
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DOS
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This file was processed as: MacBinary
(archive/macBinary ).
You can browse this item here: Hacker's Helper 1996.04 Dr. D
Confidence Program Detection Match Type Support
10%
dexvert
MacBinary (archive/macBinary)
fallback
Supported
100%
file
MacBinary II, inited, Sun Mar 31 17:37:22 1996, modified Sun Mar 31 17:37:23 1996, creator 'KRAK', type 'SNKR', 166810 bytes "Hacker's Helper 1996.04 Dr. D" , at 0x28c1a 388 bytes resource
default (weak)
99%
file
data
default
100%
TrID
MacBinary 2
default (weak)
100%
siegfried
fmt/1762 MacBinary (II)
default
100%
lsar
MacBinary
default
id metadata key value macFileType [ SNKR] macFileCreator [ KRAK]
hex view +--------+-------------------------+-------------------------+--------+--------+ |00000000| 00 1d 48 61 63 6b 65 72 | 27 73 20 48 65 6c 70 65 |..Hacker|'s Helpe| |00000010| 72 20 31 39 39 36 2e 30 | 34 20 44 72 2e 20 44 00 |r 1996.0|4 Dr. D.| |00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........| |00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........| |00000040| 00 53 4e 4b 52 4b 52 41 | 4b 01 00 00 00 00 00 00 |.SNKRKRA|K.......| |00000050| 00 00 00 00 02 8b 9a 00 | 00 01 84 ad 84 b9 a2 ad |........|........| |00000060| 84 b9 a3 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........| |00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 8e 8b 00 00 |........|........| |00000080| 43 72 61 63 6b 73 20 26 | 20 4e 75 6d 62 65 72 73 |Cracks &| Numbers| |00000090| 0d 32 0d 34 36 35 0d 33 | 2f 33 30 2f 39 36 0d 2d |.2.465.3|/30/96.-| |000000a0| 0d 2a 2a 2a 20 48 61 63 | 6b 65 72 27 73 20 48 65 |.*** Hac|ker's He| |000000b0| 6c 70 65 72 20 2a 2a 2a | 0d 76 41 6c 6c 0d a0 20 |lper ***|.vAll.. | |000000c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 48 | | H| |000000d0| 61 63 6b 65 72 27 73 20 | 48 65 6c 70 65 72 20 41 |acker's |Helper A| |000000e0| 70 72 69 6c 20 32 2c 31 | 39 39 36 0d 20 20 20 20 |pril 2,1|996. | |000000f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 2d 20 | | - | |00000100| 6e 6f 77 20 62 72 6f 75 | 67 68 74 20 74 6f 20 79 |now brou|ght to y| |00000110| 6f 75 20 62 79 0d 20 20 | 20 20 20 20 20 20 20 20 |ou by. | | |00000120| 20 20 20 20 20 20 2e 2e | 2e 2e 20 54 68 65 20 41 | ..|.. The A| |00000130| 4d 41 5a 49 4e 47 20 44 | 72 2e 20 44 20 2e 2e 2e |MAZING D|r. D ...| |00000140| 2e 0d 2d 0d 33 44 20 55 | 6c 74 72 61 20 50 69 6e |..-.3D U|ltra Pin| |00000150| 62 61 6c 6c 0d 76 31 2e | 30 0d a0 33 44 20 55 6c |ball.v1.|0..3D Ul| |00000160| 74 72 61 20 50 69 6e 62 | 61 6c 6c 20 69 73 20 61 |tra Pinb|all is a| |00000170| 20 76 65 72 79 20 65 61 | 73 79 20 67 61 6d 65 20 | very ea|sy game | |00000180| 74 6f 20 6b 72 61 6b 2e | 2e 20 0d 43 72 61 63 6b |to krak.|. .Crack| |00000190| 20 23 31 29 20 48 65 72 | 65 20 69 73 20 77 68 61 | #1) Her|e is wha| |000001a0| 74 20 79 6f 75 20 64 6f | 3a 0d 0d 4f 70 65 6e 20 |t you do|:..Open | |000001b0| 75 70 20 74 68 65 20 67 | 61 6d 65 20 77 69 74 68 |up the g|ame with| |000001c0| 20 52 65 73 45 64 69 74 | 20 61 6e 64 20 67 6f 20 | ResEdit| and go | |000001d0| 74 6f 20 53 74 72 69 6e | 67 73 0d 44 6f 75 62 6c |to Strin|gs.Doubl| |000001e0| 65 20 63 6c 69 63 6b 20 | 6f 6e 20 22 41 70 70 20 |e click |on "App | |000001f0| 53 70 65 63 69 66 69 63 | 20 53 74 72 69 6e 67 22 |Specific| String"| |00000200| 0d 47 6f 20 74 6f 20 73 | 74 72 69 6e 67 20 23 32 |.Go to s|tring #2| |00000210| 20 61 6e 64 20 65 72 61 | 73 65 20 74 68 65 20 6c | and era|se the l| |00000220| 69 6e 65 20 74 68 61 74 | 20 73 61 79 73 20 22 33 |ine that| says "3| |00000230| 44 20 55 6c 74 72 61 20 | 50 69 6e 62 61 6c 6c 20 |D Ultra |Pinball | |00000240| 43 44 22 0d 53 61 76 65 | 20 63 68 61 6e 67 65 73 |CD".Save| changes| |00000250| 20 61 6e 64 20 70 6c 61 | 79 2e 2e 2e 0d 0d 43 72 | and pla|y.....Cr| |00000260| 61 63 6b 20 23 32 29 20 | 54 6f 20 67 65 74 20 33 |ack #2) |To get 3| |00000270| 44 20 55 6c 74 72 61 20 | 50 69 6e 62 61 6c 6c 20 |D Ultra |Pinball | |00000280| 74 6f 20 72 75 6e 20 77 | 69 74 68 6f 75 74 20 74 |to run w|ithout t| |00000290| 68 65 20 43 44 20 69 73 | 20 72 65 61 6c 20 65 61 |he CD is| real ea| |000002a0| 73 79 2e 0d 0d 4f 70 65 | 6e 20 74 68 65 20 6d 61 |sy...Ope|n the ma| |000002b0| 69 6e 20 61 70 70 20 77 | 69 74 68 20 52 65 73 45 |in app w|ith ResE| |000002c0| 64 69 74 2c 20 0d 67 6f | 20 74 6f 20 53 54 52 23 |dit, .go| to STR#| |000002d0| 20 38 30 33 20 22 41 70 | 70 20 53 70 65 63 69 66 | 803 "Ap|p Specif| |000002e0| 69 63 20 53 74 72 69 6e | 67 73 22 2c 20 0d 73 74 |ic Strin|gs", .st| |000002f0| 72 69 6e 67 20 23 32 20 | 73 61 79 73 20 22 33 44 |ring #2 |says "3D| |00000300| 20 55 6c 74 72 61 20 50 | 69 6e 62 61 6c 6c 20 43 | Ultra P|inball C| |00000310| 44 22 2c 20 0d 63 68 61 | 6e 67 65 20 69 74 20 74 |D", .cha|nge it t| |00000320| 6f 20 22 3a 22 2c 20 0d | 74 68 61 74 73 20 61 20 |o ":", .|thats a | |00000330| 63 6f 6c 6f 6e 20 77 69 | 74 68 6f 75 74 20 74 68 |colon wi|thout th| |00000340| 65 20 71 75 6f 74 65 73 | 0d 0d 4e 6f 77 20 69 74 |e quotes|..Now it| |00000350| 27 6c 6c 20 72 75 6e 20 | 77 2f 6f 20 74 68 65 20 |'ll run |w/o the | |00000360| 43 44 2e 0d 2d 0d 34 44 | 20 42 61 63 6b 75 70 0d |CD..-.4D| Backup.| |00000370| 76 31 2e 35 0d 49 44 20 | 55 39 45 35 38 35 37 33 |v1.5.ID |U9E58573| |00000380| 33 38 33 54 4e 31 31 0d | 53 2f 4e 20 39 32 30 31 |383TN11.|S/N 9201| |00000390| 39 35 39 34 0d 4c 49 43 | 23 20 38 32 43 37 34 30 |9594.LIC|# 82C740| |000003a0| 45 37 45 42 36 34 43 43 | 43 44 0d 0d 2d 0d 34 44 |E7EB64CC|CD..-.4D| |000003b0| 20 42 6f 78 69 6e 67 0d | 76 31 2e 30 0d a0 43 4f | Boxing.|v1.0..CO| |000003c0| 44 45 20 31 32 20 2b 30 | 43 46 41 20 36 36 30 34 |DE 12 +0|CFA 6604| |000003d0| 2d 3e 36 30 30 34 0d 0d | 54 68 65 20 70 72 6f 67 |->6004..|The prog| |000003e0| 72 61 6d 20 77 69 6c 6c | 20 6e 65 76 65 72 20 61 |ram will| never a| |000003f0| 73 6b 20 79 6f 75 20 74 | 68 65 20 71 75 65 73 74 |sk you t|he quest| |00000400| 69 6f 6e 2e 20 2d 20 0d | 43 4f 44 45 20 31 32 2c |ion. - .|CODE 12,| |00000410| 20 6f 66 66 73 65 74 20 | 30 43 46 41 20 2d 20 63 | offset |0CFA - c| |00000420| 68 61 6e 67 65 20 36 36 | 30 34 20 74 6f 20 36 30 |hange 66|04 to 60| |00000430| 30 34 20 0d 59 6f 75 27 | 6c 6c 20 6e 65 76 65 72 |04 .You'|ll never| |00000440| 20 62 65 20 61 73 6b 65 | 64 20 74 68 65 20 62 6f | be aske|d the bo| |00000450| 78 65 72 27 73 20 6e 61 | 6d 65 20 2d 20 0d 43 4f |xer's na|me - .CO| |00000460| 44 45 20 33 2c 20 6f 66 | 66 73 65 74 20 34 30 38 |DE 3, of|fset 408| |00000470| 30 20 2d 20 63 68 61 6e | 67 65 20 30 43 46 30 20 |0 - chan|ge 0CF0 | |00000480| 46 46 46 45 20 36 36 45 | 36 20 34 45 41 44 20 30 |FFFE 66E|6 4EAD 0| |00000490| 44 36 41 20 33 30 32 44 | 20 42 43 30 41 20 45 35 |D6A 302D| BC0A E5| |000004a0| 34 30 20 0d 74 6f 20 32 | 46 30 42 20 32 46 30 43 |40 .to 2|F0B 2F0C| |000004b0| 20 33 30 32 44 20 42 43 | 30 41 20 45 35 34 30 20 | 302D BC|0A E540 | |000004c0| 32 36 37 33 20 30 30 30 | 30 20 31 38 44 42 20 20 |2673 000|0 18DB | |000004d0| 0d 43 4f 44 45 20 33 2c | 20 6f 66 66 73 65 74 20 |.CODE 3,| offset | |000004e0| 34 30 39 30 20 2d 20 63 | 68 61 6e 67 65 20 32 46 |4090 - c|hange 2F| |000004f0| 33 33 20 30 30 30 30 20 | 32 46 30 43 20 34 45 41 |33 0000 |2F0C 4EA| |00000500| 44 20 30 37 41 41 20 0d | 74 6f 20 36 36 46 43 20 |D 07AA .|to 66FC | |00000510| 32 38 35 46 20 32 36 35 | 46 20 37 30 30 30 20 34 |285F 265|F 7000 4| |00000520| 45 37 31 20 0d 2d 0d 34 | 44 20 43 6f 6d 70 69 6c |E71 .-.4|D Compil| |00000530| 65 72 0d 76 32 2e 33 0d | 76 32 2e 30 2e 34 0d 32 |er.v2.3.|v2.0.4.2| |00000540| 30 39 39 36 31 36 39 39 | 32 32 38 39 31 0d 32 30 |09961699|22891.20| |00000550| 39 39 36 31 36 39 39 32 | 33 38 38 31 0d 32 30 39 |99616992|3881.209| |00000560| 39 36 31 36 39 39 32 34 | 38 37 31 0d 32 30 39 39 |96169924|871.2099| |00000570| 36 31 36 39 39 32 35 38 | 36 31 0d 32 30 39 39 36 |61699258|61.20996| |00000580| 31 36 39 39 32 36 38 35 | 31 0d 32 30 39 39 36 31 |16992685|1.209961| |00000590| 36 39 39 32 37 38 34 31 | 0d 32 30 39 39 36 31 36 |69927841|.2099616| |000005a0| 39 39 32 38 38 33 31 0d | 32 30 39 39 36 31 36 39 |9928831.|20996169| |000005b0| 39 32 39 38 32 31 0d a0 | 46 6f 72 20 53 4e 23 20 |929821..|For SN# | |000005c0| 67 65 6e 65 72 61 74 69 | 6f 6e 20 69 6e 66 6f 20 |generati|on info | |000005d0| 73 65 65 20 74 68 65 20 | 27 34 44 20 53 65 72 69 |see the |'4D Seri| |000005e0| 61 6c 20 4e 75 6d 62 65 | 72 20 53 63 68 65 6d 65 |al Numbe|r Scheme| |000005f0| 27 20 65 6e 74 72 79 2e | 0d 0d 54 68 65 20 66 69 |' entry.|..The fi| |00000600| 72 73 74 20 74 69 6d 65 | 20 34 44 20 43 6f 6d 70 |rst time| 4D Comp| |00000610| 69 6c 65 72 20 69 73 20 | 72 75 6e 20 69 74 20 77 |iler is |run it w| |00000620| 69 6c 6c 20 61 73 6b 20 | 79 6f 75 20 66 6f 72 20 |ill ask |you for | |00000630| 61 20 73 65 72 69 61 6c | 20 6e 75 6d 62 65 72 20 |a serial| number | |00000640| 61 6e 64 20 74 68 65 6e | 20 74 6f 20 69 6e 73 65 |and then| to inse| |00000650| 72 74 20 69 74 27 73 20 | 6b 65 79 20 64 69 73 6b |rt it's |key disk| |00000660| 20 2d 20 69 74 20 77 69 | 6c 6c 20 74 68 65 6e 20 | - it wi|ll then | |00000670| 63 72 65 61 74 65 20 61 | 20 68 69 64 64 65 6e 20 |create a| hidden | |00000680| 66 69 6c 65 20 27 78 78 | 27 20 61 74 20 74 68 65 |file 'xx|' at the| |00000690| 20 72 6f 6f 74 20 6c 65 | 76 65 6c 20 6f 66 20 74 | root le|vel of t| |000006a0| 68 65 20 76 6f 6c 75 6d | 65 20 74 68 61 74 20 34 |he volum|e that 4| |000006b0| 44 20 43 6f 6d 70 69 6c | 65 72 20 69 73 20 6f 6e |D Compil|er is on| |000006c0| 20 2d 20 74 68 69 73 20 | 66 69 6c 65 20 69 73 20 | - this |file is | |000006d0| 75 73 65 64 20 69 6e 73 | 74 65 61 64 20 6f 66 20 |used ins|tead of | |000006e0| 79 6f 75 20 68 61 76 69 | 6e 67 20 74 6f 20 69 6e |you havi|ng to in| |000006f0| 73 65 72 74 20 74 68 65 | 20 6b 65 79 20 64 69 73 |sert the| key dis| |00000700| 6b 20 66 72 6f 6d 20 74 | 68 65 6e 20 6f 6e 2e 0d |k from t|hen on..| |00000710| 0d 50 72 6f 63 65 64 75 | 72 65 20 66 6f 72 20 6d |.Procedu|re for m| |00000720| 61 6b 69 6e 67 20 34 44 | 20 43 6f 6d 70 69 6c 65 |aking 4D| Compile| |00000730| 72 20 32 2e 33 20 36 38 | 4b 20 63 72 65 61 74 65 |r 2.3 68|K create| |00000740| 20 61 20 76 61 6c 69 64 | 20 78 78 20 66 69 6c 65 | a valid| xx file| |00000750| 20 75 73 69 6e 67 20 4d | 61 63 73 42 75 67 3a 0d | using M|acsBug:.| |00000760| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========| |00000770| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========| |00000780| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========| |00000790| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========| |000007a0| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 0d 23 31 |========|=====.#1| |000007b0| 29 20 4d 61 6b 65 20 61 | 20 70 68 79 73 69 63 61 |) Make a| physica| |000007c0| 6c 20 64 69 73 6b 20 69 | 6d 61 67 65 20 6f 66 20 |l disk i|mage of | |000007d0| 74 68 65 20 69 6e 73 74 | 61 6c 6c 65 72 20 64 69 |the inst|aller di| |000007e0| 73 6b 20 31 20 6f 72 20 | 68 61 76 65 20 61 6e 79 |sk 1 or |have any| |000007f0| 20 66 6f 72 6d 61 74 74 | 65 64 20 48 44 20 44 69 | formatt|ed HD Di| |00000800| 73 6b 20 68 61 6e 64 79 | 0d 0d 74 68 65 6e 20 66 |sk handy|..then f| |00000810| 6f 6c 6c 6f 77 20 74 68 | 69 73 20 70 72 6f 63 65 |ollow th|is proce| |00000820| 64 75 72 65 20 45 58 41 | 43 54 4c 59 20 28 6e 6f |dure EXA|CTLY (no| |00000830| 74 65 20 3c 63 72 3e 20 | 69 6e 64 69 63 61 74 65 |te <cr> |indicate| |00000840| 73 20 79 6f 75 20 70 72 | 65 73 73 20 72 65 74 75 |s you pr|ess retu| |00000850| 72 6e 29 0d 0d 23 32 29 | 20 44 65 6c 65 74 65 20 |rn)..#2)| Delete | |00000860| 61 6e 79 2f 61 6c 6c 20 | 6f 6c 64 20 78 78 20 28 |any/all |old xx (| |00000870| 68 69 64 64 65 6e 29 20 | 66 69 6c 65 28 73 29 20 |hidden) |file(s) | |00000880| 61 6e 64 20 43 6f 6d 70 | 69 6c 65 72 20 70 72 65 |and Comp|iler pre| |00000890| 66 73 0d 0d 23 33 29 20 | 51 75 69 74 20 61 6c 6c |fs..#3) |Quit all| |000008a0| 20 6f 74 68 65 72 20 72 | 75 6e 6e 69 6e 67 20 61 | other r|unning a| |000008b0| 70 70 6c 69 63 61 74 69 | 6f 6e 73 2e 0d 0d 23 34 |pplicati|ons...#4| |000008c0| 29 20 52 75 6e 20 34 44 | 20 43 6f 6d 70 69 6c 65 |) Run 4D| Compile| |000008d0| 72 20 32 2e 33 20 36 38 | 4b 2e 0d 0d 23 35 29 20 |r 2.3 68|K...#5) | |000008e0| 50 65 72 73 6f 6e 61 6c | 69 7a 65 20 61 6e 64 20 |Personal|ize and | |000008f0| 65 6e 74 65 72 20 61 6e | 79 20 76 61 6c 69 64 20 |enter an|y valid | |00000900| 73 65 72 69 61 6c 20 6e | 75 6d 62 65 72 20 73 75 |serial n|umber su| |00000910| 63 68 20 61 73 3a 20 27 | 32 30 39 39 36 31 36 39 |ch as: '|20996169| |00000920| 39 32 39 38 32 31 27 0d | 0d 23 36 29 20 44 69 61 |929821'.|.#6) Dia| |00000930| 6c 6f 67 20 77 69 6c 6c | 20 63 6f 6d 65 20 75 70 |log will| come up| |00000940| 20 61 73 6b 69 6e 67 20 | 66 6f 72 20 74 68 65 20 | asking |for the | |00000950| 6b 65 79 20 64 69 73 6b | 0d 0d 23 37 29 20 42 72 |key disk|..#7) Br| |00000960| 65 61 6b 20 69 6e 74 6f | 20 64 65 62 75 67 67 65 |eak into| debugge| |00000970| 72 20 61 6e 64 20 74 79 | 70 65 3a 0d 0d 09 41 54 |r and ty|pe:...AT| |00000980| 42 20 46 72 65 65 44 69 | 61 6c 6f 67 3b 47 3c 43 |B FreeDi|alog;G<C| |00000990| 52 3e 0d 09 0d 23 38 29 | 20 70 68 79 73 69 63 61 |R>...#8)| physica| |000009a0| 6c 6c 79 20 69 6e 73 65 | 72 74 20 74 68 65 20 64 |lly inse|rt the d| |000009b0| 69 73 6b 20 6d 65 6e 74 | 69 6f 6e 65 64 20 69 6e |isk ment|ioned in| |000009c0| 20 73 74 65 70 20 23 31 | 2e 0d 0d 23 39 29 20 44 | step #1|...#9) D| |000009d0| 65 62 75 67 67 65 72 20 | 77 69 6c 6c 20 6e 6f 77 |ebugger |will now| |000009e0| 20 70 6f 70 20 75 70 2e | 20 20 54 79 70 65 28 4e | pop up.| Type(N| |000009f0| 6f 74 65 3a 20 53 30 20 | 73 74 61 6e 64 73 20 66 |ote: S0 |stands f| |00000a00| 6f 72 20 73 74 65 70 2d | 6f 76 65 72 20 69 65 20 |or step-|over ie | |00000a10| 4f 20 69 6e 20 53 4f 20 | 69 73 20 61 20 6c 65 74 |O in SO |is a let| |00000a20| 74 65 72 20 6e 6f 74 20 | 7a 65 72 6f 29 3a 0d 0d |ter not |zero):..| |00000a30| 09 41 54 43 3b 53 4f 20 | 44 3b 42 52 20 3a 2b 34 |.ATC;SO |D;BR :+4| |00000a40| 30 46 32 3b 47 3c 43 52 | 3e 0d 09 0d 23 41 29 20 |0F2;G<CR|>...#A) | |00000a50| 44 65 62 75 67 67 65 72 | 20 77 69 6c 6c 20 6e 6f |Debugger| will no| |00000a60| 77 20 70 6f 70 20 75 70 | 20 61 74 20 43 4f 44 45 |w pop up| at CODE| |00000a70| 20 23 32 20 2b 34 30 46 | 32 2c 20 74 79 70 65 0d | #2 +40F|2, type.| |00000a80| 0d 09 42 52 43 3b 50 43 | 3d 50 43 2b 34 3b 47 3c |..BRC;PC|=PC+4;G<| |00000a90| 43 52 3e 0d 09 0d 23 42 | 29 20 51 75 69 74 20 61 |CR>...#B|) Quit a| |00000aa0| 6e 64 20 52 75 6e 20 61 | 67 61 69 6e 20 2d 20 77 |nd Run a|gain - w| |00000ab0| 69 6c 6c 20 6e 6f 74 20 | 61 73 6b 20 66 6f 72 20 |ill not |ask for | |00000ac0| 6b 65 79 20 64 69 73 6b | 20 61 67 61 69 6e 20 75 |key disk| again u| |00000ad0| 6e 6c 65 73 73 20 79 6f | 75 20 6d 61 64 65 20 61 |nless yo|u made a| |00000ae0| 6e 20 65 72 72 6f 72 2e | 20 20 49 66 20 73 6f 20 |n error.| If so | |00000af0| 73 74 61 72 74 20 6f 76 | 65 72 0d 2d 0d 34 44 20 |start ov|er.-.4D | |00000b00| 44 65 76 2f 52 75 6e 74 | 69 6d 65 20 4b 65 79 20 |Dev/Runt|ime Key | |00000b10| 44 69 73 6b 0d 76 33 2e | 32 20 28 36 38 4b 29 20 |Disk.v3.|2 (68K) | |00000b20| 42 79 70 61 73 73 0d 76 | 33 2e 32 20 46 69 6c 65 |Bypass.v|3.2 File| |00000b30| 20 46 6f 72 6d 61 74 0d | a0 49 6e 73 74 61 6c 6c | Format.|.Install| |00000b40| 20 74 68 65 20 36 38 4b | 20 76 65 72 73 69 6f 6e | the 68K| version| |00000b50| 20 6f 66 20 34 44 20 33 | 2e 32 20 66 72 6f 6d 20 | of 4D 3|.2 from | |00000b60| 74 68 65 20 69 6d 61 67 | 65 73 2e 0d 0d 54 68 65 |the imag|es...The| |00000b70| 20 66 69 72 73 74 20 74 | 69 6d 65 20 34 44 20 69 | first t|ime 4D i| |00000b80| 73 20 72 75 6e 20 69 74 | 20 77 69 6c 6c 20 61 73 |s run it| will as| |00000b90| 6b 20 79 6f 75 20 74 6f | 20 69 6e 73 65 72 74 20 |k you to| insert | |00000ba0| 69 74 27 73 20 6b 65 79 | 20 64 69 73 6b 20 2d 20 |it's key| disk - | |00000bb0| 69 74 20 77 69 6c 6c 20 | 74 68 65 6e 20 63 72 65 |it will |then cre| |00000bc0| 61 74 65 20 61 20 68 69 | 64 64 65 6e 20 66 69 6c |ate a hi|dden fil| |00000bd0| 65 20 27 78 62 27 20 28 | 44 65 76 65 6c 6f 70 65 |e 'xb' (|Develope| |00000be0| 72 29 20 6f 72 20 27 78 | 63 27 20 28 52 75 6e 74 |r) or 'x|c' (Runt| |00000bf0| 69 6d 65 29 20 61 74 20 | 74 68 65 20 72 6f 6f 74 |ime) at |the root| |00000c00| 20 6c 65 76 65 6c 20 6f | 66 20 74 68 65 20 76 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De| |000019a0| 6c 65 74 65 20 74 68 65 | 20 63 6f 70 79 20 61 6e |lete the| copy an| |000019b0| 64 20 72 75 6e 20 74 68 | 65 20 6f 72 69 67 69 6e |d run th|e origin| |000019c0| 61 6c 20 62 65 63 61 75 | 73 65 20 74 68 65 20 63 |al becau|se the c| |000019d0| 68 61 6e 67 65 73 0d 20 | 20 20 63 61 75 73 65 20 |hanges. | cause | |000019e0| 63 72 61 73 68 65 73 20 | 69 6e 20 74 68 65 20 70 |crashes |in the p| |000019f0| 72 6f 67 72 61 6d 2e 20 | 59 6f 75 20 77 69 6c 6c |rogram. |You will| |00001a00| 20 68 6f 77 65 76 65 72 | 20 6e 6f 20 6c 6f 6e 67 | however| no long| |00001a10| 65 72 20 62 65 20 61 73 | 6b 65 64 20 66 6f 72 0d |er be as|ked for.| |00001a20| 20 20 20 61 20 6b 65 79 | 20 64 69 73 6b 20 61 74 | a key| disk at| |00001a30| 20 73 74 61 72 74 75 70 | 2e 0d 2d 0d 34 44 20 49 | startup|..-.4D I| |00001a40| 6e 73 69 64 65 72 0d 76 | 32 2e 30 2e 31 0d 31 31 |nsider.v|2.0.1.11| |00001a50| 33 30 35 39 37 30 39 31 | 31 34 39 31 0d 2d 0d 34 |30597091|1491.-.4| |00001a60| 44 20 4f 6e 6c 69 6e 65 | 20 48 65 6c 70 0d 76 33 |D Online| Help.v3| |00001a70| 2e 30 2e 35 0d 31 32 33 | 34 35 36 34 30 30 0d 36 |.0.5.123|456400.6| |00001a80| 35 34 33 32 31 33 30 31 | 0d 0d a0 54 68 65 20 53 |54321301|...The S| |00001a90| 4e 23 20 61 6c 67 6f 72 | 69 74 68 6d 20 69 73 20 |N# algor|ithm is | |00001aa0| 61 73 20 66 6f 6c 6c 6f | 77 73 3a 0d 0d 6e 75 6d |as follo|ws:..num| |00001ab0| 31 3d 46 69 72 73 74 20 | 73 69 78 20 64 69 67 69 |1=First |six digi| |00001ac0| 74 73 20 6f 66 20 74 68 | 65 20 73 65 72 69 61 6c |ts of th|e serial| |00001ad0| 20 6e 75 6d 62 65 72 0d | 6e 75 6d 32 3d 28 28 6e | number.|num2=((n| |00001ae0| 75 6d 31 25 37 29 2a 31 | 30 30 29 2b 28 28 6e 75 |um1%7)*1|00)+((nu| |00001af0| 6d 31 25 33 29 2a 31 30 | 29 2b 28 6e 75 6d 31 25 |m1%3)*10|)+(num1%| |00001b00| 32 29 0d 0d 53 4e 23 3d | 3c 6e 75 6d 31 3e 3c 6e |2)..SN#=|<num1><n| |00001b10| 75 6d 32 3e 0d 0d 54 68 | 75 73 20 69 66 20 6e 75 |um2>..Th|us if nu| |00001b20| 6d 31 3d 36 35 34 33 32 | 31 2c 20 6e 75 6d 32 3d |m1=65432|1, num2=| |00001b30| 28 33 2a 31 30 30 29 2b | 28 30 2a 31 30 29 2b 28 |(3*100)+|(0*10)+(| |00001b40| 31 29 3d 33 30 31 20 73 | 6f 20 53 4e 23 3d 27 36 |1)=301 s|o SN#='6| |00001b50| 35 34 33 32 31 33 30 31 | 27 0d 0d 4e 6f 74 65 3a |54321301|'..Note:| |00001b60| 20 6f 6e 6c 79 20 74 68 | 65 20 6e 75 6d 65 72 69 | only th|e numeri| |00001b70| 63 61 6c 20 76 61 6c 75 | 65 20 6f 66 20 3c 6e 75 |cal valu|e of <nu| |00001b80| 6d 32 3e 20 69 73 20 73 | 69 67 6e 69 66 69 63 61 |m2> is s|ignifica| |00001b90| 6e 74 2c 20 73 6f 20 77 | 65 20 63 6f 75 6c 64 20 |nt, so w|e could | |00001ba0| 61 6c 73 6f 20 75 73 65 | 20 27 36 35 34 33 32 31 |also use| '654321| |00001bb0| 30 30 30 30 30 30 33 30 | 31 27 0d 2d 0d 34 44 20 |00000030|1'.-.4D | |00001bc0| 52 75 6e 74 69 6d 65 0d | 76 33 2e 32 0d a0 46 6f |Runtime.|v3.2..Fo| |00001bd0| 72 20 6b 65 79 20 64 69 | 73 6b 20 69 6e 66 6f 20 |r key di|sk info | |00001be0| 73 65 65 20 74 68 65 20 | 65 6e 74 72 79 3a 20 27 |see the |entry: '| |00001bf0| 34 44 20 44 65 76 2f 52 | 75 6e 74 69 6d 65 20 4b |4D Dev/R|untime K| |00001c00| 65 79 20 44 69 73 6b 27 | 0d 0d 46 6f 72 20 53 4e |ey Disk'|..For SN| |00001c10| 23 20 67 65 6e 65 72 61 | 74 69 6f 6e 20 69 6e 66 |# genera|tion inf| |00001c20| 6f 20 73 65 65 20 74 68 | 65 20 65 6e 74 72 79 3a |o see th|e entry:| |00001c30| 20 27 34 44 20 53 65 72 | 69 61 6c 20 4e 75 6d 62 | '4D Ser|ial Numb| |00001c40| 65 72 20 53 63 68 65 6d | 65 27 0d 2d 0d 34 44 20 |er Schem|e'.-.4D | |00001c50| 53 65 72 69 61 6c 20 4e | 75 6d 62 65 72 20 53 63 |Serial N|umber Sc| |00001c60| 68 65 6d 65 0d 76 56 61 | 72 69 6f 75 73 0d a0 34 |heme.vVa|rious..4| |00001c70| 44 20 53 4e 23 20 53 63 | 68 65 6d 65 20 49 6e 66 |D SN# Sc|heme Inf| |00001c80| 6f 0d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |o.======|========| |00001c90| 3d 3d 3d 3d 0d 0d 54 68 | 65 20 66 6f 6c 6c 6f 77 |====..Th|e follow| |00001ca0| 69 6e 67 20 69 73 20 43 | 20 28 6f 72 20 69 6e 20 |ing is C| (or in | |00001cb0| 74 68 65 20 6c 61 74 65 | 72 20 63 61 73 65 73 20 |the late|r cases | |00001cc0| 70 73 65 75 64 6f 29 20 | 63 6f 64 65 20 74 6f 20 |pseudo) |code to | |00001cd0| 67 65 6e 65 72 61 74 65 | 20 61 6e 64 2f 6f 72 20 |generate| and/or | |00001ce0| 63 68 65 63 6b 20 34 74 | 68 20 44 69 6d 65 6e 73 |check 4t|h Dimens| |00001cf0| 69 6f 6e 20 73 65 72 69 | 61 6c 20 6e 75 6d 62 65 |ion seri|al numbe| |00001d00| 72 73 2e 20 20 54 68 69 | 73 20 69 6e 66 6f 72 6d |rs. Thi|s inform| |00001d10| 61 74 69 6f 6e 20 61 70 | 70 6c 69 65 73 20 74 6f |ation ap|plies to| |00001d20| 20 74 68 65 20 66 6f 6c | 6c 6f 77 69 6e 67 20 70 | the fol|lowing p| |00001d30| 72 6f 64 75 63 74 73 2c | 20 77 68 6f 73 65 20 6d |roducts,| whose m| |00001d40| 69 6e 4c 65 6e 67 74 68 | 20 61 6e 64 20 6d 75 6c |inLength| and mul| |00001d50| 74 20 70 61 72 61 6d 61 | 74 65 72 73 20 61 72 65 |t parama|ters are| |00001d60| 20 6c 69 73 74 65 64 3a | 0d 0d 50 72 6f 64 75 63 | listed:|..Produc| |00001d70| 74 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |t | | |00001d80| 20 6d 69 6e 4c 65 6e 67 | 74 68 20 6d 75 6c 74 0d | minLeng|th mult.| |00001d90| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========| |00001da0| 20 20 20 20 20 20 20 3d | 3d 3d 3d 3d 3d 3d 3d 3d | =|========| |00001db0| 20 3d 3d 3d 3d 0d 34 44 | 20 49 6e 73 69 64 65 72 | ====.4D| Insider| |00001dc0| 20 31 2e 30 2e 31 20 20 | 20 20 20 20 20 34 20 20 | 1.0.1 | 4 | |00001dd0| 20 20 20 20 20 20 20 35 | 0d 34 44 20 49 6e 73 69 | 5|.4D Insi| |00001de0| 64 65 72 20 32 2e 30 2e | 31 20 20 20 20 20 20 20 |der 2.0.|1 | |00001df0| 34 20 20 20 20 20 20 20 | 20 20 35 39 20 77 68 69 |4 | 59 whi| |00001e00| 63 68 20 69 73 20 65 71 | 75 69 76 61 6c 65 6e 74 |ch is eq|uivalent| |00001e10| 20 74 6f 20 39 20 73 69 | 6e 63 65 20 28 61 2b 62 | to 9 si|nce (a+b| |00001e20| 29 25 63 3d 28 61 2b 28 | 62 25 63 29 29 25 63 0d |)%c=(a+(|b%c))%c.| |00001e30| 34 44 20 43 6f 6d 70 69 | 6c 65 72 20 32 2e 33 20 |4D Compi|ler 2.3 | |00001e40| 20 20 20 20 20 20 20 38 | 20 20 20 20 20 20 20 20 | 8| | |00001e50| 20 37 0d 34 44 20 52 75 | 6e 74 69 6d 65 20 33 2e | 7.4D Ru|ntime 3.| |00001e60| 32 20 20 20 20 20 20 20 | 20 20 38 20 20 20 20 20 |2 | 8 | |00001e70| 20 20 20 20 32 0d 34 44 | 20 44 65 76 65 6c 6f 70 | 2.4D| Develop| |00001e80| 65 72 20 33 2e 32 20 20 | 20 20 20 20 20 38 20 20 |er 3.2 | 8 | |00001e90| 20 20 20 20 20 20 20 30 | 0d 0d 2f 2a 20 2a 2a 2a | 0|../* ***| |00001ea0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00001eb0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00001ec0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00001ed0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00001ee0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00001ef0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 20 2a 2f 0d 69 |********|*** */.i| |00001f00| 6e 74 09 6d 79 56 61 6c | 28 63 68 61 72 20 63 29 |nt.myVal|(char c)| |00001f10| 0d 7b 0d 09 72 65 74 75 | 72 6e 20 28 63 3e 3d 27 |.{..retu|rn (c>='| |00001f20| 41 27 29 3f 63 2d 27 41 | 27 2b 31 30 3a 63 2d 27 |A')?c-'A|'+10:c-'| |00001f30| 30 27 3b 20 2f 2f 20 4d | 61 70 20 27 30 27 2e 2e |0'; // M|ap '0'..| |00001f40| 27 39 27 2c 27 41 27 2e | 2e 27 5a 27 20 74 6f 20 |'9','A'.|.'Z' to | |00001f50| 30 2e 2e 33 35 20 28 69 | 65 20 74 72 65 61 74 20 |0..35 (i|e treat | |00001f60| 61 73 20 62 61 73 65 20 | 33 36 29 0d 7d 0d 2f 2a |as base |36).}./*| |00001f70| 20 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a | *******|********| |00001f80| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00001f90| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00001fa0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00001fb0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00001fc0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 20 |********|******* | |00001fd0| 2a 2f 0d 63 68 61 72 20 | 6d 79 56 61 6c 54 6f 43 |*/.char |myValToC| |00001fe0| 68 61 72 28 73 68 6f 72 | 74 20 76 29 0d 7b 0d 09 |har(shor|t v).{..| |00001ff0| 72 65 74 75 72 6e 20 28 | 76 3e 39 29 3f 27 41 27 |return (|v>9)?'A'| |00002000| 2b 76 2d 31 30 3a 27 30 | 27 2b 76 3b 0d 7d 0d 0d |+v-10:'0|'+v;.}..| |00002010| 2f 2a 20 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |/* *****|********| |00002020| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002030| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002040| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002050| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002060| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002070| 2a 20 2a 2f 0d 42 6f 6f | 6c 65 61 6e 20 69 73 56 |* */.Boo|lean isV| |00002080| 61 6c 69 64 53 4e 28 53 | 74 72 69 6e 67 50 74 72 |alidSN(S|tringPtr| |00002090| 20 53 4e 53 74 72 3b 73 | 68 6f 72 74 20 6d 69 6e | SNStr;s|hort min| |000020a0| 4c 65 6e 67 74 68 3b 73 | 68 6f 72 74 20 6d 75 6c |Length;s|hort mul| |000020b0| 74 29 0d 7b 0d 0d 73 68 | 6f 72 74 09 6c 65 6e 2c |t).{..sh|ort.len,| |000020c0| 6d 69 64 2c 69 2c 6b 0d | 63 68 61 72 09 73 70 65 |mid,i,k.|char.spe| |000020d0| 63 69 61 6c 41 2c 73 70 | 65 63 69 61 6c 42 2c 73 |cialA,sp|ecialB,s| |000020e0| 70 65 63 69 61 6c 43 0d | 42 6f 6f 6c 65 61 6e 09 |pecialC.|Boolean.| |000020f0| 69 73 56 61 6c 69 64 3d | 54 52 55 45 3b 0d 0d 09 |isValid=|TRUE;...| |00002100| 6c 65 6e 3d 53 4e 53 74 | 72 5b 30 5d 3b 0d 09 69 |len=SNSt|r[0];..i| |00002110| 66 20 28 6c 65 6e 3e 3d | 6d 69 6e 4c 65 6e 67 74 |f (len>=|minLengt| |00002120| 68 29 0d 09 7b 0d 09 09 | 6d 69 64 3d 6c 65 6e 2f |h)..{...|mid=len/| |00002130| 32 3b 0d 09 09 73 70 65 | 63 69 61 6c 41 3d 6d 79 |2;...spe|cialA=my| |00002140| 56 61 6c 28 53 4e 53 74 | 72 5b 6c 65 6e 5d 29 0d |Val(SNSt|r[len]).| |00002150| 09 09 53 70 65 63 69 61 | 6c 42 3d 28 28 6d 79 56 |..Specia|lB=((myV| |00002160| 61 6c 28 53 4e 53 74 72 | 5b 6c 65 6e 2d 31 5d 29 |al(SNStr|[len-1])| |00002170| 5e 73 70 65 63 69 61 6c | 41 29 2b 6d 69 64 29 25 |^special|A)+mid)%| |00002180| 31 30 3b 0d 09 09 69 3d | 31 3b 0d 09 09 77 68 69 |10;...i=|1;...whi| |00002190| 6c 65 20 28 28 69 73 56 | 61 6c 69 64 29 26 26 28 |le ((isV|alid)&&(| |000021a0| 69 3c 6d 69 64 29 29 2f | 2f 6e 6f 74 65 3a 20 49 |i<mid))/|/note: I| |000021b0| 66 20 6c 65 6e 20 69 73 | 20 6f 64 64 20 69 6d 70 |f len is| odd imp| |000021c0| 6c 69 65 73 20 74 68 61 | 74 20 53 4e 53 74 72 5b |lies tha|t SNStr[| |000021d0| 4c 65 6e 2d 33 5d 20 69 | 73 20 61 72 62 69 74 72 |Len-3] i|s arbitr| |000021e0| 61 72 79 0d 09 09 7b 0d | 09 09 09 6b 3d 6d 69 64 |ary...{.|...k=mid| |000021f0| 2d 69 3b 0d 09 09 09 73 | 70 65 63 69 61 6c 43 3d |-i;....s|pecialC=| |00002200| 28 6d 79 56 61 6c 28 53 | 4e 53 74 72 5b 32 2a 69 |(myVal(S|NStr[2*i| |00002210| 5d 29 5e 73 70 65 63 69 | 61 6c 41 29 25 31 30 3b |])^speci|alA)%10;| |00002220| 0d 0d 09 09 09 2f 2f 6e | 6f 74 65 20 74 68 69 73 |.....//n|ote this| |00002230| 20 6e 65 78 74 20 74 65 | 73 74 20 62 61 73 69 63 | next te|st basic| |00002240| 61 6c 6c 79 20 69 6d 70 | 6c 69 65 73 20 74 68 61 |ally imp|lies tha| |00002250| 74 20 69 73 41 6c 70 68 | 61 28 53 4e 53 74 72 5b |t isAlph|a(SNStr[| |00002260| 6b 5d 29 3d 69 73 41 6c | 70 68 61 28 53 4e 53 74 |k])=isAl|pha(SNSt| |00002270| 72 5b 32 2a 6b 2d 31 5d | 29 0d 09 09 09 2f 2f 61 |r[2*k-1]|)....//a| |00002280| 73 20 66 61 72 20 61 73 | 20 74 68 65 20 70 72 6f |s far as| the pro| |00002290| 74 65 63 74 69 6f 6e 20 | 64 65 73 69 67 6e 65 72 |tection |designer| |000022a0| 73 20 69 6e 74 65 6e 74 | 69 6f 6e 73 20 67 6f 65 |s intent|ions goe| |000022b0| 73 2e 20 20 48 6f 77 65 | 76 65 72 20 74 68 65 20 |s. Howe|ver the | |000022c0| 63 6f 64 65 20 74 68 61 | 74 0d 09 09 09 2f 2f 63 |code tha|t....//c| |000022d0| 68 65 63 6b 73 20 74 68 | 65 20 73 65 72 69 61 6c |hecks th|e serial| |000022e0| 20 6e 75 6d 62 65 72 20 | 77 69 6c 6c 20 61 63 74 | number |will act| |000022f0| 75 61 6c 6c 79 20 61 63 | 63 65 70 74 20 61 20 6c |ually ac|cept a l| |00002300| 61 72 67 65 72 20 73 65 | 72 69 61 6c 20 6e 75 6d |arger se|rial num| |00002310| 62 65 72 20 64 6f 6d 61 | 69 6e 0d 09 09 09 2f 2f |ber doma|in....//| |00002320| 74 68 61 74 20 69 73 20 | 70 6f 73 73 69 62 6c 65 |that is |possible| |00002330| 20 77 68 65 6e 20 74 68 | 69 73 20 72 75 6c 65 20 | when th|is rule | |00002340| 69 73 20 6e 6f 74 20 66 | 6f 6c 6c 6f 77 65 64 20 |is not f|ollowed | |00002350| 61 6e 64 2f 6f 72 20 6e | 6f 6e 20 30 2d 39 2c 41 |and/or n|on 0-9,A| |00002360| 2d 5a 20 63 68 61 72 61 | 63 74 65 72 73 20 61 72 |-Z chara|cters ar| |00002370| 65 0d 09 09 09 2f 2f 75 | 73 65 64 20 66 6f 72 20 |e....//u|sed for | |00002380| 69 6e 73 74 61 6e 63 65 | 20 27 3a 27 20 77 6f 75 |instance| ':' wou| |00002390| 6c 64 20 62 65 20 69 6e | 74 65 72 70 72 65 74 65 |ld be in|terprete| |000023a0| 64 20 61 73 20 61 20 6e | 75 6d 62 65 72 20 61 6e |d as a n|umber an| |000023b0| 64 20 68 61 76 65 20 61 | 20 76 61 6c 75 65 20 6f |d have a| value o| |000023c0| 66 20 31 30 0d 0d 09 09 | 09 69 66 20 28 53 4e 53 |f 10....|.if (SNS| |000023d0| 74 72 5b 6b 5d 3e 3d 27 | 41 27 29 20 2f 2f 20 54 |tr[k]>='|A') // T| |000023e0| 68 69 73 20 74 61 6b 65 | 73 20 6d 61 6b 65 73 20 |his take|s makes | |000023f0| 69 6e 76 65 72 74 69 6e | 67 20 74 68 69 73 20 72 |invertin|g this r| |00002400| 6f 75 74 69 6e 65 20 6e | 6f 6e 2d 74 72 69 76 69 |outine n|on-trivi| |00002410| 61 6c 0d 09 09 09 09 73 | 70 65 63 69 61 6c 42 3d |al.....s|pecialB=| |00002420| 28 28 28 53 4e 53 74 72 | 5b 32 2a 6b 2d 31 5d 2d |(((SNStr|[2*k-1]-| |00002430| 27 41 27 2b 31 30 29 5e | 73 70 65 63 69 61 6c 41 |'A'+10)^|specialA| |00002440| 29 2b 6b 2b 73 70 65 63 | 69 61 6c 42 2b 28 69 2a |)+k+spec|ialB+(i*| |00002450| 6d 75 6c 74 29 29 25 31 | 30 3b 0d 09 09 09 65 6c |mult))%1|0;....el| |00002460| 73 65 0d 09 09 09 09 73 | 70 65 63 69 61 6c 42 3d |se.....s|pecialB=| |00002470| 28 28 28 53 4e 53 74 72 | 5b 32 2a 6b 2d 31 5d 2d |(((SNStr|[2*k-1]-| |00002480| 27 30 27 20 20 20 29 5e | 73 70 65 63 69 61 6c 41 |'0' )^|specialA| |00002490| 29 2b 6b 2b 73 70 65 63 | 69 61 6c 42 2b 28 69 2a |)+k+spec|ialB+(i*| |000024a0| 6d 75 6c 74 29 29 25 31 | 30 3b 0d 0d 09 09 09 69 |mult))%1|0;.....i| |000024b0| 73 56 61 6c 69 64 3d 28 | 73 70 65 63 69 61 6c 42 |sValid=(|specialB| |000024c0| 3d 3d 73 70 65 63 69 61 | 6c 43 29 0d 09 09 09 69 |==specia|lC)....i| |000024d0| 2b 2b 3b 0d 09 09 7d 0d | 20 20 20 20 7d 0d 20 20 |++;...}.| }. | |000024e0| 20 20 65 6c 73 65 20 69 | 73 56 61 6c 69 64 3d 46 | else i|sValid=F| |000024f0| 41 4c 53 45 3b 0d 09 72 | 65 74 75 72 6e 20 69 73 |ALSE;..r|eturn is| |00002500| 56 61 6c 69 64 3b 0d 7d | 0d 2f 2a 20 2a 2a 2a 2a |Valid;.}|./* ****| |00002510| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002520| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002530| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002540| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002550| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002560| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 20 2a 2f 0d 2f 2a |********|** */./*| |00002570| 20 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a | *******|********| |00002580| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002590| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |000025a0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |000025b0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |000025c0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 20 |********|******* | |000025d0| 2a 2f 0d 2f 2a 20 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |*/./* **|********| |000025e0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |000025f0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002600| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002610| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002620| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00002630| 2a 2a 2a 2a 20 2a 2f 0d | 49 20 77 69 6c 6c 20 70 |**** */.|I will p| |00002640| 72 65 73 65 6e 74 20 74 | 77 6f 20 65 6e 74 69 72 |resent t|wo entir| |00002650| 65 6c 79 20 64 69 66 66 | 65 72 65 6e 74 20 6d 65 |ely diff|erent me| |00002660| 74 68 6f 64 73 20 66 6f | 72 20 67 65 6e 65 72 61 |thods fo|r genera| |00002670| 74 69 6e 67 20 73 65 72 | 69 61 6c 20 6e 75 6d 62 |ting ser|ial numb| |00002680| 65 72 73 2e 20 20 54 68 | 65 20 73 69 6d 70 6c 65 |ers. Th|e simple| |00002690| 73 74 2c 20 6d 6f 73 74 | 20 64 69 72 65 63 74 20 |st, most| direct | |000026a0| 6d 65 74 68 6f 64 20 6f | 66 20 61 74 74 61 63 6b |method o|f attack| |000026b0| 20 69 73 20 74 6f 20 72 | 65 73 74 72 69 63 74 20 | is to r|estrict | |000026c0| 74 68 65 20 70 72 6f 62 | 6c 65 6d 20 64 6f 6d 61 |the prob|lem doma| |000026d0| 69 6e 20 74 6f 20 74 68 | 61 74 20 6f 66 20 65 6e |in to th|at of en| |000026e0| 74 69 72 65 6c 79 20 6e | 75 6d 65 72 69 63 20 73 |tirely n|umeric s| |000026f0| 65 72 69 61 6c 20 6e 75 | 6d 62 65 72 73 2e 20 20 |erial nu|mbers. | |00002700| 54 68 69 73 20 61 70 70 | 72 6f 61 63 68 20 72 65 |This app|roach re| |00002710| 6d 6f 76 65 73 20 74 68 | 65 20 64 69 66 66 69 63 |moves th|e diffic| |00002720| 75 6c 74 79 20 69 6d 70 | 6f 73 65 64 20 62 79 20 |ulty imp|osed by | |00002730| 74 68 65 20 22 28 53 4e | 53 74 72 5b 6b 5d 3e 3d |the "(SN|Str[k]>=| |00002740| 27 41 27 29 22 20 74 65 | 73 74 20 2d 20 62 75 74 |'A')" te|st - but| |00002750| 20 69 6d 70 6f 73 65 73 | 20 74 68 65 20 6c 65 73 | imposes| the les| |00002760| 73 65 72 20 72 65 73 74 | 72 69 63 74 69 6f 6e 20 |ser rest|riction | |00002770| 74 68 61 74 20 53 4e 53 | 74 72 5b 4c 65 6e 5d 20 |that SNS|tr[Len] | |00002780| 69 73 20 27 30 27 20 6f | 72 20 27 31 27 20 69 6e |is '0' o|r '1' in| |00002790| 20 67 65 6e 65 72 61 6c | 20 28 73 70 65 63 69 66 | general| (specif| |000027a0| 69 63 20 63 6f 75 6e 74 | 65 72 65 78 61 6d 70 6c |ic count|erexampl| |000027b0| 65 73 20 65 78 69 73 74 | 29 2e 20 20 54 68 75 73 |es exist|). Thus| |000027c0| 20 77 65 20 63 61 6e 20 | 61 72 62 69 74 72 61 72 | we can |arbitrar| |000027d0| 69 6c 79 20 63 68 6f 6f | 73 65 20 64 69 67 69 74 |ily choo|se digit| |000027e0| 73 20 66 6f 72 20 74 68 | 65 20 66 69 72 73 74 20 |s for th|e first | |000027f0| 28 6d 69 64 2d 31 29 20 | 6f 64 64 20 69 6e 64 65 |(mid-1) |odd inde| |00002800| 78 20 63 68 61 72 61 63 | 74 65 72 73 2c 20 74 68 |x charac|ters, th| |00002810| 65 20 32 6e 64 20 74 6f | 20 6c 61 73 74 20 28 6c |e 2nd to| last (l| |00002820| 65 6e 2d 31 29 20 63 68 | 61 72 61 63 74 65 72 20 |en-1) ch|aracter | |00002830| 28 61 63 74 75 61 6c 6c | 79 20 74 68 69 73 20 63 |(actuall|y this c| |00002840| 68 61 72 61 63 74 65 72 | 20 63 61 6e 20 65 76 65 |haracter| can eve| |00002850| 6e 20 62 65 20 61 6e 20 | 61 6c 70 68 61 29 2c 20 |n be an |alpha), | |00002860| 77 68 69 6c 65 20 74 68 | 65 20 6c 61 73 74 20 63 |while th|e last c| |00002870| 68 61 72 61 63 74 65 72 | 20 69 73 20 63 68 6f 6f |haracter| is choo| |00002880| 73 65 6e 20 61 73 20 27 | 30 27 20 6f 72 20 27 31 |sen as '|0' or '1| |00002890| 27 2e 20 20 4f 6e 63 65 | 20 74 68 6f 73 65 20 63 |'. Once| those c| |000028a0| 68 6f 69 63 65 73 20 68 | 61 76 65 20 62 65 65 6e |hoices h|ave been| |000028b0| 20 6d 61 64 65 20 69 74 | 20 69 73 20 61 20 66 61 | made it| is a fa| |000028c0| 69 72 6c 79 20 73 74 72 | 61 69 67 68 74 20 66 6f |irly str|aight fo| |000028d0| 72 77 61 72 64 20 70 72 | 6f 63 65 64 75 72 65 20 |rward pr|ocedure | |000028e0| 74 6f 20 63 61 6c 63 75 | 6c 61 74 65 20 74 68 65 |to calcu|late the| |000028f0| 20 72 65 6d 61 69 6e 69 | 6e 67 20 66 69 72 73 74 | remaini|ng first| |00002900| 20 28 6d 69 64 2d 31 29 | 20 65 76 65 6e 20 69 6e | (mid-1)| even in| |00002910| 64 65 78 20 6e 75 6d 65 | 72 69 63 20 63 68 61 72 |dex nume|ric char| |00002920| 61 63 74 65 72 73 2e 20 | 20 54 68 65 20 70 72 6f |acters. | The pro| |00002930| 63 65 64 75 72 65 20 69 | 73 20 61 73 20 66 6f 6c |cedure i|s as fol| |00002940| 6c 6f 77 73 0d 0d 53 74 | 65 70 0d 3d 3d 3d 3d 0d |lows..St|ep.====.| |00002950| 0d 23 31 20 43 68 6f 6f | 73 65 20 6c 65 6e 20 73 |.#1 Choo|se len s| |00002960| 75 63 68 20 74 68 61 74 | 20 6c 65 6e 3e 3d 6d 69 |uch that| len>=mi| |00002970| 6e 4c 65 6e 67 74 68 20 | 61 6e 64 20 6c 65 6e 25 |nLength |and len%| |00002980| 32 3d 30 0d 23 32 20 53 | 65 74 20 6d 69 64 3d 6c |2=0.#2 S|et mid=l| |00002990| 65 6e 2f 32 0d 23 33 20 | 43 68 6f 6f 73 65 20 6e |en/2.#3 |Choose n| |000029a0| 75 6d 65 72 69 63 20 63 | 68 61 72 61 63 74 65 72 |umeric c|haracter| |000029b0| 73 20 74 6f 20 6f 63 63 | 75 70 79 20 74 68 65 20 |s to occ|upy the | |000029c0| 66 69 72 73 74 20 28 6d | 69 64 2d 31 29 20 6f 64 |first (m|id-1) od| |000029d0| 64 20 69 6e 64 65 78 20 | 70 6f 73 69 74 69 6f 6e |d index |position| |000029e0| 73 20 6f 66 20 53 4e 53 | 74 72 0d 23 34 20 43 68 |s of SNS|tr.#4 Ch| |000029f0| 6f 6f 73 65 20 6e 75 6d | 65 72 69 63 20 6f 72 20 |oose num|eric or | |00002a00| 61 6c 70 68 61 20 63 68 | 61 72 61 63 74 65 72 20 |alpha ch|aracter | |00002a10| 74 6f 20 6f 63 63 75 70 | 79 20 53 4e 53 74 72 5b |to occup|y SNStr[| |00002a20| 6c 65 6e 2d 31 5d 0d 23 | 35 20 43 68 6f 6f 73 65 |len-1].#|5 Choose| |00002a30| 20 6e 75 6d 65 72 69 63 | 20 63 68 61 72 61 63 74 | numeric| charact| |00002a40| 65 72 20 27 30 27 20 6f | 72 20 27 31 27 20 74 6f |er '0' o|r '1' to| |00002a50| 20 6f 63 63 75 70 79 20 | 53 4e 53 74 72 5b 6c 65 | occupy |SNStr[le| |00002a60| 6e 5d 0d 23 36 20 69 66 | 20 6c 65 6e 25 32 3d 31 |n].#6 if| len%2=1| |00002a70| 20 28 6c 65 6e 20 69 73 | 20 6f 64 64 29 20 74 68 | (len is| odd) th| |00002a80| 65 6e 20 63 68 6f 6f 73 | 65 20 61 6e 20 61 72 62 |en choos|e an arb| |00002a90| 69 74 72 61 72 79 20 63 | 68 61 72 61 63 74 65 72 |itrary c|haracter| |00002aa0| 20 66 6f 72 20 53 4e 53 | 74 72 5b 6c 65 6e 2d 33 | for SNS|tr[len-3| |00002ab0| 5d 0d 23 37 20 43 61 6c | 63 75 6c 61 74 65 20 74 |].#7 Cal|culate t| |00002ac0| 68 65 20 63 6f 6e 73 74 | 61 6e 74 20 20 20 20 20 |he const|ant | |00002ad0| 20 20 20 20 73 70 65 63 | 69 61 6c 41 3d 20 20 6d | spec|ialA= m| |00002ae0| 79 56 61 6c 28 53 4e 53 | 74 72 5b 6c 65 6e 5d 29 |yVal(SNS|tr[len])| |00002af0| 0d 23 38 20 43 61 6c 63 | 75 6c 61 74 65 20 74 68 |.#8 Calc|ulate th| |00002b00| 65 20 69 6e 69 74 69 61 | 6c 20 76 61 6c 75 65 20 |e initia|l value | |00002b10| 6f 66 20 73 70 65 63 69 | 61 6c 42 3d 28 28 6d 79 |of speci|alB=((my| |00002b20| 56 61 6c 28 53 4e 53 74 | 72 5b 6c 65 6e 2d 31 5d |Val(SNSt|r[len-1]| |00002b30| 29 5e 73 70 65 63 69 61 | 6c 41 29 2b 6d 69 64 29 |)^specia|lA)+mid)| |00002b40| 25 31 30 0d 23 39 20 53 | 65 74 20 69 3d 30 0d 23 |%10.#9 S|et i=0.#| |00002b50| 41 20 20 20 49 6e 63 72 | 65 6d 65 6e 74 20 69 20 |A Incr|ement i | |00002b60| 74 68 65 6e 20 73 65 74 | 20 6b 3d 6d 69 64 2d 69 |then set| k=mid-i| |00002b70| 0d 23 42 20 20 20 43 61 | 6c 63 75 6c 61 74 65 20 |.#B Ca|lculate | |00002b80| 73 70 65 63 69 61 6c 42 | 3d 28 28 28 53 4e 53 74 |specialB|=(((SNSt| |00002b90| 72 5b 32 2a 6b 2d 31 5d | 2d 27 30 27 29 5e 73 70 |r[2*k-1]|-'0')^sp| |00002ba0| 65 63 69 61 6c 41 29 2b | 6b 2b 73 70 65 63 69 61 |ecialA)+|k+specia| |00002bb0| 6c 42 2b 28 69 2a 6d 75 | 6c 74 29 29 25 31 30 0d |lB+(i*mu|lt))%10.| |00002bc0| 0d 20 20 20 20 20 41 74 | 20 74 68 69 73 20 70 6f |. At| this po| |00002bd0| 69 6e 74 20 77 65 20 6b | 6e 6f 77 20 74 68 61 74 |int we k|now that| |00002be0| 20 30 3c 3d 73 70 65 63 | 69 61 6c 41 3c 32 20 61 | 0<=spec|ialA<2 a| |00002bf0| 6e 64 20 30 3c 3d 73 70 | 65 63 69 61 6c 42 3c 31 |nd 0<=sp|ecialB<1| |00002c00| 30 0d 20 20 20 20 20 57 | 65 20 6e 65 65 64 20 74 |0. W|e need t| |00002c10| 6f 20 66 69 6e 64 20 74 | 68 65 20 76 61 6c 75 65 |o find t|he value| |00002c20| 20 6f 66 20 43 3d 6d 79 | 56 61 6c 28 53 4e 53 74 | of C=my|Val(SNSt| |00002c30| 72 5b 32 2a 69 5d 29 20 | 73 75 63 68 20 74 68 61 |r[2*i]) |such tha| |00002c40| 74 0d 0d 20 20 20 20 20 | 28 43 5e 73 70 65 63 69 |t.. |(C^speci| |00002c50| 61 6c 41 29 25 31 30 3d | 73 70 65 63 69 61 6c 42 |alA)%10=|specialB| |00002c60| 2c 20 43 3d 30 2e 2e 39 | 2e 0d 0d 20 20 20 20 20 |, C=0..9|... | |00002c70| 4c 65 74 74 69 6e 67 20 | 44 3d 43 5e 73 70 65 63 |Letting |D=C^spec| |00002c80| 69 61 6c 41 20 74 68 65 | 20 61 62 6f 76 65 20 6d |ialA the| above m| |00002c90| 6f 64 75 6c 61 72 20 65 | 71 75 61 74 69 6f 6e 20 |odular e|quation | |00002ca0| 62 65 63 6f 6d 65 73 20 | 44 25 31 30 3d 73 70 65 |becomes |D%10=spe| |00002cb0| 63 69 61 6c 42 2c 20 43 | 3d 30 2e 2e 39 0d 0d 20 |cialB, C|=0..9.. | |00002cc0| 20 20 20 20 54 68 65 20 | 67 65 6e 65 72 61 6c 20 | The |general | |00002cd0| 73 6f 6c 75 74 69 6f 6e | 20 28 74 68 65 20 65 71 |solution| (the eq| |00002ce0| 75 61 74 69 6f 6e 20 68 | 61 73 20 73 6f 6c 75 74 |uation h|as solut| |00002cf0| 69 6f 6e 73 20 73 69 6e | 63 65 20 73 70 65 63 69 |ions sin|ce speci| |00002d00| 61 6c 42 3c 31 30 29 20 | 74 6f 20 74 68 69 73 20 |alB<10) |to this | |00002d10| 6d 6f 64 75 6c 61 72 20 | 65 71 75 61 74 69 6f 6e |modular |equation| |00002d20| 0d 20 20 20 20 20 69 73 | 3a 0d 0d 20 20 20 20 20 |. is|:.. | |00002d30| 44 3d 73 70 65 63 69 61 | 6c 42 20 2b 20 31 30 2a |D=specia|lB + 10*| |00002d40| 6d 2c 20 69 6e 74 65 67 | 65 72 20 6d 3d 30 2e 2e |m, integ|er m=0..| |00002d50| 69 6e 66 69 6e 69 74 79 | 2e 0d 0d 20 20 20 20 20 |infinity|... | |00002d60| 48 6f 77 65 76 65 72 20 | 73 69 6e 63 65 20 77 65 |However |since we| |00002d70| 20 6d 75 73 74 20 68 61 | 76 65 20 43 3d 30 2e 2e | must ha|ve C=0..| |00002d80| 39 20 28 69 6e 20 6f 72 | 64 65 72 20 74 6f 20 67 |9 (in or|der to g| |00002d90| 65 74 20 61 20 6e 75 6d | 65 72 69 63 20 53 4e 23 |et a num|eric SN#| |00002da0| 29 20 61 6e 64 20 73 70 | 65 63 69 61 6c 41 3d 30 |) and sp|ecialA=0| |00002db0| 2e 2e 31 20 77 65 20 6b | 6e 6f 77 0d 20 20 20 20 |..1 we k|now. | |00002dc0| 20 74 68 61 74 20 44 3d | 30 2e 2e 39 20 73 69 6e | that D=|0..9 sin| |00002dd0| 63 65 20 44 3d 43 5e 73 | 70 65 63 69 61 6c 41 20 |ce D=C^s|pecialA | |00002de0| 61 6e 64 20 39 5e 31 3d | 38 3c 31 30 20 61 6e 64 |and 9^1=|8<10 and| |00002df0| 20 61 2d 62 3c 3d 30 3c | 3d 61 5e 62 3c 3d 61 2b | a-b<=0<|=a^b<=a+| |00002e00| 62 20 2c 20 77 68 65 6e | 20 30 3c 3d 62 3c 3d 61 |b , when| 0<=b<=a| |00002e10| 0d 20 20 20 20 20 28 69 | 65 20 44 3d 30 2e 2e 39 |. (i|e D=0..9| |00002e20| 20 73 69 6e 63 65 20 30 | 2e 2e 39 20 78 6f 72 20 | since 0|..9 xor | |00002e30| 30 2e 2e 31 3d 30 2e 2e | 39 2c 20 62 75 74 20 30 |0..1=0..|9, but 0| |00002e40| 2e 2e 39 20 78 6f 72 20 | 32 2e 2e 6d 3d 30 2e 2e |..9 xor |2..m=0..| |00002e50| 39 2b 6d 20 2d 2d 20 74 | 68 69 73 20 69 73 20 74 |9+m -- t|his is t| |00002e60| 68 65 20 72 65 61 73 6f | 6e 20 77 68 79 0d 20 20 |he reaso|n why. | |00002e70| 20 20 20 73 70 65 63 69 | 61 6c 41 20 28 61 6e 64 | speci|alA (and| |00002e80| 20 74 68 75 73 20 74 68 | 65 20 6c 61 73 74 20 63 | thus th|e last c| |00002e90| 68 61 72 61 63 74 65 72 | 29 20 6d 75 73 74 20 62 |haracter|) must b| |00002ea0| 65 20 72 65 73 74 72 69 | 63 74 65 64 20 74 6f 20 |e restri|cted to | |00002eb0| 30 2e 2e 31 29 0d 0d 20 | 20 20 20 20 54 68 75 73 |0..1).. | Thus| |00002ec0| 20 73 69 6e 63 65 20 77 | 65 20 6b 6e 6f 77 20 74 | since w|e know t| |00002ed0| 68 61 74 20 44 3d 30 2e | 2e 39 20 77 65 20 63 61 |hat D=0.|.9 we ca| |00002ee0| 6e 20 69 67 6e 6f 72 65 | 20 74 68 65 20 6d 6f 64 |n ignore| the mod| |00002ef0| 20 6f 70 65 72 61 74 6f | 72 20 61 6e 64 20 77 6f | operato|r and wo| |00002f00| 72 6b 20 77 69 74 68 20 | 74 68 65 20 73 69 6d 70 |rk with |the simp| |00002f10| 6c 65 20 65 71 75 61 74 | 69 6f 6e 0d 0d 20 20 20 |le equat|ion.. | |00002f20| 20 20 44 3d 73 70 65 63 | 69 61 6c 42 20 6f 72 20 | D=spec|ialB or | |00002f30| 43 5e 73 70 65 63 69 61 | 6c 41 3d 73 70 65 63 69 |C^specia|lA=speci| |00002f40| 61 6c 42 20 77 68 69 63 | 68 20 69 6d 70 6c 69 65 |alB whic|h implie| |00002f50| 73 20 43 3d 73 70 65 63 | 69 61 6c 42 5e 73 70 65 |s C=spec|ialB^spe| |00002f60| 63 69 61 6c 41 20 74 68 | 75 73 20 77 65 20 68 61 |cialA th|us we ha| |00002f70| 76 65 20 73 74 65 70 20 | 23 43 0d 0d 23 43 20 20 |ve step |#C..#C | |00002f80| 20 43 61 6c 63 75 6c 61 | 74 65 20 74 68 65 20 73 | Calcula|te the s| |00002f90| 6f 6c 75 74 69 6f 6e 20 | 63 68 61 72 61 63 74 65 |olution |characte| |00002fa0| 72 20 61 73 20 53 4e 53 | 74 72 5b 32 2a 69 5d 3d |r as SNS|tr[2*i]=| |00002fb0| 6d 79 56 61 6c 54 6f 43 | 68 61 72 28 73 70 65 63 |myValToC|har(spec| |00002fc0| 69 61 6c 42 5e 73 70 65 | 63 69 61 6c 41 29 0d 23 |ialB^spe|cialA).#| |00002fd0| 44 20 20 20 69 66 20 28 | 69 3c 6d 69 64 29 20 67 |D if (|i<mid) g| |00002fe0| 6f 74 6f 20 73 74 65 70 | 20 23 41 0d 0d 45 78 61 |oto step| #A..Exa| |00002ff0| 6d 70 6c 65 20 66 6f 72 | 20 6c 65 6e 3d 31 34 2c |mple for| len=14,| |00003000| 20 6d 75 6c 74 3d 39 0d | 0d 43 68 61 72 20 20 20 | mult=9.|.Char | |00003010| 20 20 20 30 30 30 30 30 | 30 30 30 30 30 31 31 31 | 00000|00000111| |00003020| 31 31 0d 49 6e 64 65 78 | 20 20 20 20 20 30 31 32 |11.Index| 012| |00003030| 33 34 35 36 37 38 39 30 | 31 32 33 34 0d 20 20 20 |34567890|1234. | |00003040| 20 20 20 20 20 20 20 2d | 2d 2d 2d 2d 2d 2d 2d 2d | -|--------| |00003050| 2d 2d 2d 2d 2d 2d 0d 53 | 4e 53 74 72 5b 5d 3d 22 |------.S|NStr[]="| |00003060| 5c 70 31 23 33 23 35 23 | 37 23 39 23 31 23 39 31 |\p1#3#5#|7#9#1#91| |00003070| 22 0d 0d 41 66 74 65 72 | 20 53 74 65 70 20 41 0d |"..After| Step A.| |00003080| 0d 6d 69 64 3d 37 0d 73 | 70 65 63 69 61 6c 41 3d |.mid=7.s|pecialA=| |00003090| 6d 79 56 61 6c 28 27 31 | 27 29 3d 31 0d 73 70 65 |myVal('1|')=1.spe| |000030a0| 63 69 61 6c 42 3d 28 28 | 39 5e 31 29 2b 37 29 25 |cialB=((|9^1)+7)%| |000030b0| 31 30 3d 28 38 2b 37 29 | 25 31 30 3d 35 0d 0d 41 |10=(8+7)|%10=5..A| |000030c0| 66 74 65 72 20 53 74 65 | 70 20 43 20 28 69 3d 31 |fter Ste|p C (i=1| |000030d0| 2c 6b 3d 36 29 0d 73 70 | 65 63 69 61 6c 42 3d 28 |,k=6).sp|ecialB=(| |000030e0| 28 28 27 31 27 2d 27 30 | 27 29 5e 31 29 2b 36 2b |(('1'-'0|')^1)+6+| |000030f0| 35 2b 39 29 25 31 30 3d | 28 30 2b 32 30 29 25 31 |5+9)%10=|(0+20)%1| |00003100| 30 3d 31 30 25 31 30 3d | 30 0d 53 4e 53 74 72 5b |0=10%10=|0.SNStr[| |00003110| 32 5d 3d 6d 79 56 61 6c | 54 6f 43 68 61 72 28 30 |2]=myVal|ToChar(0| |00003120| 5e 31 29 3d 27 31 27 0d | 0d 41 66 74 65 72 20 53 |^1)='1'.|.After S| |00003130| 74 65 70 20 43 20 28 69 | 3d 32 2c 6b 3d 35 29 0d |tep C (i|=2,k=5).| |00003140| 73 70 65 63 69 61 6c 42 | 3d 28 28 28 27 39 27 2d |specialB|=((('9'-| |00003150| 27 30 27 29 5e 31 29 2b | 35 2b 30 2b 38 29 25 31 |'0')^1)+|5+0+8)%1| |00003160| 30 3d 28 28 39 5e 31 29 | 2b 31 33 29 25 31 30 3d |0=((9^1)|+13)%10=| |00003170| 32 31 25 31 30 3d 31 20 | 2f 2f 38 20 69 73 20 6a |21%10=1 |//8 is j| |00003180| 75 73 74 20 31 38 25 31 | 30 20 28 6d 6f 64 75 6c |ust 18%1|0 (modul| |00003190| 61 72 20 73 69 6d 70 6c | 69 66 69 63 61 74 69 6f |ar simpl|ificatio| |000031a0| 6e 29 0d 53 4e 53 74 72 | 5b 34 5d 3d 6d 79 56 61 |n).SNStr|[4]=myVa| |000031b0| 6c 54 6f 43 68 61 72 28 | 31 5e 31 29 3d 27 30 27 |lToChar(|1^1)='0'| |000031c0| 0d 0d 41 66 74 65 72 20 | 53 74 65 70 20 43 20 28 |..After |Step C (| |000031d0| 69 3d 33 2c 6b 3d 34 29 | 0d 73 70 65 63 69 61 6c |i=3,k=4)|.special| |000031e0| 42 3d 28 28 28 27 37 27 | 2d 27 30 27 29 5e 31 29 |B=((('7'|-'0')^1)| |000031f0| 2b 34 2b 31 2b 37 29 25 | 31 30 3d 28 28 37 5e 31 |+4+1+7)%|10=((7^1| |00003200| 29 2b 31 32 29 25 31 30 | 3d 31 38 25 31 30 3d 38 |)+12)%10|=18%10=8| |00003210| 0d 53 4e 53 74 72 5b 36 | 5d 3d 6d 79 56 61 6c 54 |.SNStr[6|]=myValT| |00003220| 6f 43 68 61 72 28 38 5e | 31 29 3d 27 39 27 0d 0d |oChar(8^|1)='9'..| |00003230| 41 66 74 65 72 20 53 74 | 65 70 20 43 20 28 69 3d |After St|ep C (i=| |00003240| 34 2c 6b 3d 33 29 0d 73 | 70 65 63 69 61 6c 42 3d |4,k=3).s|pecialB=| |00003250| 28 28 28 27 35 27 2d 27 | 30 27 29 5e 31 29 2b 33 |((('5'-'|0')^1)+3| |00003260| 2b 38 2b 36 29 25 31 30 | 3d 28 28 35 5e 31 29 2b |+8+6)%10|=((5^1)+| |00003270| 31 37 29 25 31 30 3d 32 | 31 25 31 30 3d 31 0d 53 |17)%10=2|1%10=1.S| |00003280| 4e 53 74 72 5b 38 5d 3d | 6d 79 56 61 6c 54 6f 43 |NStr[8]=|myValToC| |00003290| 68 61 72 28 31 5e 31 29 | 3d 27 30 27 0d 0d 41 66 |har(1^1)|='0'..Af| |000032a0| 74 65 72 20 53 74 65 70 | 20 43 20 28 69 3d 35 2c |ter Step| C (i=5,| |000032b0| 6b 3d 32 29 0d 73 70 65 | 63 69 61 6c 42 3d 28 28 |k=2).spe|cialB=((| |000032c0| 28 27 33 27 2d 27 30 27 | 29 5e 31 29 2b 32 2b 31 |('3'-'0'|)^1)+2+1| |000032d0| 2b 35 29 25 31 30 3d 28 | 28 33 5e 31 29 2b 38 29 |+5)%10=(|(3^1)+8)| |000032e0| 25 31 30 3d 31 30 25 31 | 30 3d 30 0d 53 4e 53 74 |%10=10%1|0=0.SNSt| |000032f0| 72 5b 31 30 5d 3d 6d 79 | 56 61 6c 54 6f 43 68 61 |r[10]=my|ValToCha| |00003300| 72 28 30 5e 31 29 3d 27 | 31 27 0d 0d 41 66 74 65 |r(0^1)='|1'..Afte| |00003310| 72 20 53 74 65 70 20 43 | 20 28 69 3d 36 2c 6b 3d |r Step C| (i=6,k=| |00003320| 31 29 0d 73 70 65 63 69 | 61 6c 42 3d 28 28 28 27 |1).speci|alB=((('| |00003330| 31 27 2d 27 30 27 29 5e | 31 29 2b 31 2b 30 2b 34 |1'-'0')^|1)+1+0+4| |00003340| 29 25 31 30 3d 28 28 31 | 5e 31 29 2b 35 29 25 31 |)%10=((1|^1)+5)%1| |00003350| 30 3d 35 25 31 30 3d 35 | 0d 53 4e 53 74 72 5b 31 |0=5%10=5|.SNStr[1| |00003360| 32 5d 3d 6d 79 56 61 6c | 54 6f 43 68 61 72 28 35 |2]=myVal|ToChar(5| |00003370| 5e 31 29 3d 27 34 27 0d | 0d 74 68 75 73 20 53 4e |^1)='4'.|.thus SN| |00003380| 53 74 72 5b 5d 3d 22 5c | 70 31 31 33 30 35 39 37 |Str[]="\|p1130597| |00003390| 30 39 31 31 34 39 31 22 | 20 28 54 68 69 73 20 69 |0911491"| (This i| |000033a0| 73 20 61 20 76 61 6c 69 | 64 20 49 6e 73 69 64 65 |s a vali|d Inside| |000033b0| 72 20 32 2e 30 2e 31 20 | 53 4e 23 29 0d 0d 2f 2a |r 2.0.1 |SN#)../*| |000033c0| 20 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a | *******|********| |000033d0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |000033e0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |000033f0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00003400| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********| |00003410| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 20 |********|******* | |00003420| 2a 2f 0d 54 68 65 20 6e | 65 78 74 20 6d 65 74 68 |*/.The n|ext meth| |00003430| 6f 64 20 49 20 70 72 65 | 73 65 6e 74 20 67 65 74 |od I pre|sent get| |00003440| 73 20 61 72 6f 75 6e 64 | 20 74 68 65 20 6e 6f 20 |s around| the no | |00003450| 6e 6f 6e 2d 64 69 67 69 | 74 20 63 68 61 72 61 63 |non-digi|t charac| |00003460| 74 65 72 73 20 28 62 75 | 74 20 6c 61 73 74 20 63 |ters (bu|t last c| |00003470| 68 61 72 61 63 74 65 72 | 20 6d 75 73 74 20 62 65 |haracter| must be| |00003480| 20 61 20 27 30 27 20 6f | 72 20 27 31 27 29 20 72 | a '0' o|r '1') r| |00003490| 65 73 74 72 69 63 74 69 | 6f 6e 20 61 74 20 74 68 |estricti|on at th| |000034a0| 65 20 63 6f 73 74 20 74 | 68 61 74 20 77 65 20 6d |e cost t|hat we m| |000034b0| 75 73 74 20 77 6f 72 6b | 20 74 68 65 20 70 72 6f |ust work| the pro| |000034c0| 62 6c 65 6d 20 62 6f 74 | 68 20 66 6f 72 77 61 72 |blem bot|h forwar| |000034d0| 64 73 20 61 6e 64 20 62 | 61 63 6b 77 61 72 64 73 |ds and b|ackwards| |000034e0| 2e 20 20 54 68 69 73 20 | 74 65 63 68 6e 69 71 75 |. This |techniqu| |000034f0| 65 20 63 6f 6d 65 73 20 | 61 62 6f 75 74 20 62 79 |e comes |about by| |00003500| 20 6e 6f 74 69 6e 67 20 | 74 68 61 74 20 74 68 65 | noting |that the| |00003510| 20 22 28 53 4e 53 74 72 | 5b 6b 5d 3e 3d 27 41 27 | "(SNStr|[k]>='A'| |00003520| 29 22 20 74 65 73 74 20 | 69 73 20 6f 6e 6c 79 20 |)" test |is only | |00003530| 64 65 70 65 6e 64 65 6e | 74 20 75 70 6f 6e 20 74 |dependen|t upon t| |00003540| 68 65 20 66 69 72 73 74 | 20 28 6d 69 64 2d 31 29 |he first| (mid-1)| |00003550| 20 63 68 61 72 61 63 74 | 65 72 73 20 6f 66 20 53 | charact|ers of S| |00003560| 4e 53 74 72 2e 20 20 54 | 68 75 73 20 69 66 20 77 |NStr. T|hus if w| |00003570| 65 20 61 72 62 69 74 72 | 61 72 69 6c 79 20 73 65 |e arbitr|arily se| |00003580| 6c 65 63 74 20 74 68 65 | 20 6c 61 73 74 20 74 77 |lect the| last tw| |00003590| 6f 20 61 6e 64 20 74 68 | 65 73 65 20 63 68 61 72 |o and th|ese char| |000035a0| 61 63 74 65 72 73 20 77 | 69 74 68 69 6e 20 74 68 |acters w|ithin th| |000035b0| 65 20 72 65 73 74 72 69 | 63 74 69 6f 6e 28 73 29 |e restri|ction(s)| |000035c0| 20 74 68 69 73 20 74 65 | 73 74 20 69 6d 70 6f 73 | this te|st impos| |000035d0| 65 73 20 77 65 20 63 61 | 6e 20 73 6f 6c 76 65 20 |es we ca|n solve | |000035e0| 66 6f 72 20 74 68 65 20 | 72 65 6d 61 69 6e 69 6e |for the |remainin| |000035f0| 67 20 28 6e 65 78 74 20 | 6d 69 64 2d 31 29 20 63 |g (next |mid-1) c| |00003600| 68 61 72 61 63 74 65 72 | 73 20 69 6e 20 61 20 74 |haracter|s in a t| |00003610| 77 6f 20 70 61 72 74 20 | 70 72 6f 63 65 73 73 2e |wo part |process.| |00003620| 0d 0d 46 69 72 73 74 20 | 77 65 20 6d 75 73 74 20 |..First |we must | |00003630| 6e 6f 74 65 20 74 68 61 | 74 20 74 68 65 20 74 65 |note tha|t the te| |00003640| 73 74 20 69 6d 70 6c 69 | 65 73 20 74 68 61 74 3a |st impli|es that:| |00003650| 20 20 69 73 41 6c 70 68 | 61 28 53 4e 53 74 72 5b | isAlph|a(SNStr[| |00003660| 6b 5d 29 3d 69 73 41 6c | 70 68 61 28 53 4e 53 74 |k])=isAl|pha(SNSt| |00003670| 72 5b 32 2a 6b 2d 31 5d | 29 0d 0d 69 65 20 66 6f |r[2*k-1]|)..ie fo| |00003680| 72 20 4c 65 6e 3d 31 34 | 0d 0d 6b 20 32 2a 6b 2d |r Len=14|..k 2*k-| |00003690| 31 0d 3d 20 3d 3d 3d 3d | 3d 0d 36 20 31 31 0d 35 |1.= ====|=.6 11.5| |000036a0| 20 20 39 0d 34 20 20 37 | 0d 33 20 20 35 0d 32 20 | 9.4 7|.3 5.2 | |000036b0| 20 33 0d 31 20 20 31 0d | 0d 74 68 75 73 20 66 6f | 3.1 1.|.thus fo| |000036c0| 72 20 4c 65 6e 3d 31 34 | 0d 0d 43 68 61 72 20 20 |r Len=14|..Char | |000036d0| 20 20 20 20 30 30 30 30 | 30 30 30 30 30 30 31 31 | 0000|00000011| |000036e0| 31 31 31 0d 49 6e 64 65 | 78 20 20 20 20 20 30 31 |111.Inde|x 01| |000036f0| 32 33 34 35 36 37 38 39 | 30 31 32 33 34 0d 20 20 |23456789|01234. | |00003700| 20 20 20 20 20 20 20 20 | 2d 2d 2d 2d 2d 2d 2d 2d | |--------| |00003710| 2d 2d 2d 2d 2d 2d 2d 0d | 53 4e 53 74 72 5b 5d 3d |-------.|SNStr[]=| |00003720| 22 5c 70 3f 78 78 79 78 | 7a 79 3f 78 3f 7a 3f 3f |"\p?xxyx|zy?x?z??| |00003730| 3f 22 0d 0d 77 68 65 72 | 65 20 65 61 63 68 20 63 |?"..wher|e each c| |00003740| 68 61 72 61 63 74 65 72 | 20 6d 61 72 6b 65 64 20 |haracter| marked | |00003750| 77 69 74 68 20 61 6e 64 | 20 78 2c 79 2c 20 6f 72 |with and| x,y, or| |00003760| 20 7a 20 6d 75 73 74 20 | 62 65 20 74 68 65 20 73 | z must |be the s| |00003770| 61 6d 65 20 74 79 70 65 | 20 28 61 6c 70 68 61 20 |ame type| (alpha | |00003780| 6f 72 20 64 69 67 69 74 | 29 20 61 73 20 74 68 65 |or digit|) as the| |00003790| 20 6f 74 68 65 72 20 63 | 68 61 72 61 63 74 65 72 | other c|haracter| |000037a0| 73 20 73 6f 20 6d 61 72 | 6b 65 64 2e 20 49 6e 20 |s so mar|ked. In | |000037b0| 74 68 69 73 20 63 61 73 | 65 2c 20 77 65 20 61 72 |this cas|e, we ar| |000037c0| 65 20 6f 6e 6c 79 20 63 | 68 6f 6f 73 69 6e 67 20 |e only c|hoosing | |000037d0| 74 68 65 20 66 69 72 73 | 74 20 36 20 63 68 61 72 |the firs|t 6 char| |000037e0| 61 63 74 65 72 73 2c 20 | 73 6f 20 77 65 20 6d 75 |acters, |so we mu| |000037f0| 73 74 20 62 65 20 73 75 | 72 65 20 74 68 61 74 20 |st be su|re that | |00003800| 74 68 65 20 63 68 61 72 | 61 63 74 65 72 73 20 61 |the char|acters a| |00003810| 74 20 69 6e 64 65 78 65 | 73 20 32 2c 33 20 61 6e |t indexe|s 2,3 an| |00003820| 64 20 35 20 61 72 65 20 | 65 69 74 68 65 72 20 61 |d 5 are |either a| |00003830| 6c 6c 20 64 69 67 69 74 | 73 20 6f 72 20 61 6c 6c |ll digit|s or all| |00003840| 20 61 6c 70 68 61 27 73 | 20 2d 20 61 6e 64 20 77 | alpha's| - and w| |00003850| 68 65 6e 20 77 65 20 61 | 72 65 20 73 6f 6c 76 69 |hen we a|re solvi| |00003860| 6e 67 20 66 6f 72 20 74 | 68 65 20 6e 65 78 74 20 |ng for t|he next | |00003870| 73 69 78 20 63 68 61 72 | 61 63 74 65 72 73 20 77 |six char|acters w| |00003880| 65 20 6d 75 73 74 20 72 | 65 73 74 72 69 63 74 20 |e must r|estrict | |00003890| 6f 75 72 20 73 6f 6c 75 | 74 69 6f 6e 73 20 74 6f |our solu|tions to| |000038a0| 20 74 68 6f 73 65 20 69 | 6e 20 77 68 69 63 68 20 | those i|n which | |000038b0| 74 68 65 20 63 68 61 72 | 61 63 74 65 72 73 20 61 |the char|acters a| |000038c0| 74 20 69 6e 64 65 78 65 | 73 20 37 2c 39 2c 20 61 |t indexe|s 7,9, a| |000038d0| 6e 64 20 31 31 20 6d 61 | 74 63 68 20 74 68 6f 73 |nd 11 ma|tch thos| |000038e0| 65 20 74 68 61 74 20 77 | 65 20 63 68 6f 6f 73 65 |e that w|e choose| |000038f0| 20 61 74 20 34 2c 35 20 | 61 6e 64 20 36 20 72 65 | at 4,5 |and 6 re| |00003900| 73 70 65 63 74 69 76 65 | 6c 79 2e 20 20 4e 6f 77 |spective|ly. Now| |00003910| 20 61 73 20 66 61 72 20 | 61 73 20 73 6f 6c 76 69 | as far |as solvi| |00003920| 6e 67 20 66 6f 72 20 6f | 75 72 20 36 20 72 65 6d |ng for o|ur 6 rem| |00003930| 61 69 6e 69 6e 67 20 75 | 6e 6b 6e 6f 77 6e 73 20 |aining u|nknowns | |00003940| 61 74 20 70 6f 73 69 74 | 69 6f 6e 73 20 37 20 74 |at posit|ions 7 t| |00003950| 68 72 75 20 31 32 20 77 | 65 20 6e 6f 74 65 20 74 |hru 12 w|e note t| |00003960| 68 61 74 20 77 65 20 6d | 75 73 74 20 77 6f 72 6b |hat we m|ust work| |00003970| 20 74 68 65 20 69 6e 64 | 65 78 65 73 20 69 6e 20 | the ind|exes in | |00003980| 74 68 65 20 73 61 6d 65 | 20 6f 72 64 65 72 20 61 |the same| order a| |00003990| 73 20 6f 75 72 20 6c 6f | 6f 70 20 73 69 6e 63 65 |s our lo|op since| |000039a0| 20 73 70 65 63 69 61 6c | 42 20 69 73 20 61 6e 20 | special|B is an | |000039b0| 28 6d 6f 64 75 6c 61 72 | 29 20 72 65 63 75 72 72 |(modular|) recurr| |000039c0| 65 6e 63 65 20 65 71 75 | 61 74 69 6f 6e 2e 20 20 |ence equ|ation. | |000039d0| 54 68 75 73 2c 20 73 69 | 6e 63 65 20 74 68 65 20 |Thus, si|nce the | |000039e0| 69 6e 64 65 78 20 69 6e | 74 65 72 64 65 70 65 6e |index in|terdepen| |000039f0| 64 65 6e 63 69 65 73 20 | 62 65 74 77 65 65 6e 20 |dencies |between | |00003a00| 73 70 65 63 69 61 6c 42 | 20 61 6e 64 20 73 70 65 |specialB| and spe| |00003a10| 63 69 61 6c 43 20 61 72 | 65 20 28 72 65 73 70 65 |cialC ar|e (respe| |00003a20| 63 74 69 76 65 6c 79 20 | 2d 20 69 6e 20 74 68 65 |ctively |- in the| |00003a30| 20 6f 72 64 65 72 20 77 | 65 20 6d 75 73 74 20 73 | order w|e must s| |00003a40| 6f 6c 76 65 20 74 68 65 | 6d 29 3a 0d 0d 73 74 65 |olve the|m):..ste| |00003a50| 70 20 20 32 2a 6b 2d 31 | 20 32 2a 69 0d 3d 3d 3d |p 2*k-1| 2*i.===| |00003a60| 3d 20 20 3d 3d 3d 3d 3d | 20 3d 3d 3d 0d 31 20 20 |= =====| ===.1 | |00003a70| 20 20 20 31 31 20 20 20 | 20 20 32 0d 32 20 20 20 | 11 | 2.2 | |00003a80| 20 20 20 39 20 20 20 20 | 20 34 0d 33 20 20 20 20 | 9 | 4.3 | |00003a90| 20 20 37 20 20 20 20 20 | 36 0d 34 20 20 20 20 20 | 7 |6.4 | |00003aa0| 20 35 20 20 20 20 20 38 | 0d 35 20 20 20 20 20 20 | 5 8|.5 | |00003ab0| 33 20 20 20 20 31 30 0d | 36 20 20 20 20 20 20 31 |3 10.|6 1| |00003ac0| 20 20 20 20 31 32 0d 0d | 61 6e 64 20 77 65 20 68 | 12..|and we h| |00003ad0| 61 76 65 20 61 6c 72 65 | 61 64 79 20 73 70 65 63 |ave alre|ady spec| |00003ae0| 69 66 69 65 64 20 74 68 | 65 20 63 68 61 72 61 63 |ified th|e charac| |00003af0| 74 65 72 73 20 61 74 20 | 69 6e 64 65 78 65 73 20 |ters at |indexes | |00003b00| 31 20 74 68 72 75 20 36 | 20 69 74 20 69 73 20 63 |1 thru 6| it is c| |00003b10| 6c 65 61 72 20 74 68 61 | 74 20 77 65 20 6d 75 73 |lear tha|t we mus| |00003b20| 74 20 66 69 72 73 74 20 | 73 6f 6c 76 65 20 28 62 |t first |solve (b| |00003b30| 61 63 6b 77 61 72 64 73 | 29 20 66 6f 72 20 74 68 |ackwards|) for th| |00003b40| 65 20 63 68 61 72 61 63 | 74 65 72 73 20 61 74 20 |e charac|ters at | |00003b50| 70 6f 73 69 74 69 6f 6e | 73 20 31 31 2c 39 20 61 |position|s 11,9 a| |00003b60| 6e 64 20 37 20 62 79 20 | 63 61 6c 63 75 6c 61 74 |nd 7 by |calculat| |00003b70| 69 6e 67 20 73 70 65 63 | 69 61 6c 42 20 61 73 20 |ing spec|ialB as | |00003b80| 61 20 66 75 6e 63 74 69 | 6f 6e 20 6f 66 20 69 74 |a functi|on of it| |00003b90| 73 65 6c 66 20 61 6e 64 | 20 73 70 65 63 69 61 6c |self and| special| |00003ba0| 43 20 61 6e 64 20 73 70 | 65 63 69 61 6c 41 3b 20 |C and sp|ecialA; | |00003bb0| 74 68 65 6e 20 77 65 20 | 6d 75 73 74 20 73 6f 6c |then we |must sol| |00003bc0| 76 65 20 28 66 6f 72 77 | 61 72 64 73 29 20 66 6f |ve (forw|ards) fo| |00003bd0| 72 20 70 6f 73 69 74 69 | 6f 6e 73 20 38 2c 31 30 |r positi|ons 8,10| |00003be0| 20 61 6e 64 20 31 32 20 | 62 79 20 05 28 64 69 72 | and 12 |by .(dir| |00003bf0| 65 63 74 29 20 63 61 6c | 63 75 6c 61 74 69 6f 6e |ect) cal|culation| |00003c00| 20 6f 66 20 73 70 65 63 | 69 61 6c 42 20 66 72 6f | of spec|ialB fro| |00003c10| 6d 20 69 74 73 65 6c 66 | 20 61 6e 64 20 73 70 65 |m itself| and spe| |00003c20| 63 69 61 6c 41 2e 20 20 | 42 6f 74 68 20 6f 66 20 |cialA. |Both of | |00003c30| 74 68 65 73 65 20 63 61 | 6c 63 75 6c 61 74 69 6f |these ca|lculatio| |00003c40| 6e 73 20 63 61 6e 20 6c | 65 61 64 20 74 6f 20 6d |ns can l|ead to m| |00003c50| 75 6c 74 69 70 6c 65 20 | 73 6f 6c 75 74 69 6f 6e |ultiple |solution| |00003c60| 73 20 28 77 68 69 63 68 | 20 69 73 20 66 69 6e 65 |s (which| is fine| |00003c70| 29 20 64 75 65 20 74 6f | 20 6d 6f 64 75 6c 61 72 |) due to| modular| |00003c80| 20 61 72 69 74 68 6d 65 | 74 69 63 20 61 6e 64 20 | arithme|tic and | |00003c90| 74 68 65 20 69 6e 63 72 | 65 61 73 65 64 20 64 65 |the incr|eased de| |00003ca0| 67 72 65 65 73 20 6f 66 | 20 66 72 65 65 64 6f 6d |grees of| freedom| |00003cb0| 20 69 6e 20 74 68 65 20 | 70 73 65 75 64 6f 20 28 | in the |pseudo (| |00003cc0| 73 69 6e 63 65 20 74 68 | 65 20 66 69 72 73 74 20 |since th|e first | |00003cd0| 36 20 63 68 61 72 61 63 | 74 65 72 73 20 61 72 65 |6 charac|ters are| |00003ce0| 20 6e 6f 74 20 69 6e 64 | 65 70 65 6e 64 65 6e 74 | not ind|ependent| |00003cf0| 20 6f 66 20 74 68 65 6d | 73 65 6c 76 65 73 29 20 | of them|selves) | |00003d00| 69 6e 64 65 70 65 6e 64 | 65 6e 74 20 76 61 72 69 |independ|ent vari| |00003d10| 61 62 6c 65 73 20 28 63 | 68 61 72 61 63 74 65 72 |ables (c|haracter| |00003d20| 73 29 2e 0d 0d 57 65 20 | 6d 75 73 74 20 61 6c 73 |s)...We |must als| |00003d30| 6f 20 6e 6f 74 65 20 74 | 68 61 74 20 69 6e 20 67 |o note t|hat in g| |00003d40| 65 6e 65 72 61 6c 20 77 | 65 20 6d 75 73 74 20 68 |eneral w|e must h| |00003d50| 61 76 65 20 73 70 65 63 | 69 61 6c 41 3d 6d 79 56 |ave spec|ialA=myV| |00003d60| 61 6c 28 53 6e 53 74 72 | 5b 6c 65 6e 5d 29 20 69 |al(SnStr|[len]) i| |00003d70| 6e 20 61 20 73 6d 61 6c | 6c 20 65 6e 6f 75 67 68 |n a smal|l enough| |00003d80| 20 72 61 6e 67 65 20 30 | 2e 2e 6e 20 74 68 61 74 | range 0|..n that| |00003d90| 20 77 69 6c 6c 20 61 6c | 6c 6f 77 20 75 73 20 74 | will al|low us t| |00003da0| 6f 20 73 6f 6c 76 65 20 | 65 71 75 61 74 69 6f 6e |o solve |equation| |00003db0| 73 20 6f 66 20 74 68 65 | 20 66 6f 72 6d 3a 0d 0d |s of the| form:..| |00003dc0| 20 75 20 2b 20 28 76 5e | 73 70 65 63 69 61 6c 41 | u + (v^|specialA| |00003dd0| 29 3d 77 20 6d 6f 64 20 | 31 30 20 66 6f 72 20 74 |)=w mod |10 for t| |00003de0| 68 65 20 76 61 72 69 61 | 62 6c 65 20 76 3d 30 2e |he varia|ble v=0.| |00003df0| 2e 39 20 6f 72 20 31 30 | 2e 2e 33 35 20 6f 72 20 |.9 or 10|..35 or | |00003e00| 30 2e 2e 33 35 20 77 68 | 65 72 65 20 62 6f 74 68 |0..35 wh|ere both| |00003e10| 20 75 2c 77 3d 30 2e 2e | 39 0d 20 75 20 2b 20 78 | u,w=0..|9. u + x| |00003e20| 20 20 20 20 20 20 20 20 | 20 20 20 3d 77 20 6d 6f | | =w mo| |00003e30| 64 20 31 30 20 2c 77 68 | 65 72 65 20 78 3d 76 5e |d 10 ,wh|ere x=v^| |00003e40| 73 70 65 63 69 61 6c 41 | 0d 28 75 20 2b 20 78 29 |specialA|.(u + x)| |00003e50| 25 31 30 20 20 20 20 20 | 20 20 3d 77 20 20 20 20 |%10 | =w | |00003e60| 20 20 20 20 2c 77 68 69 | 63 68 20 69 6d 70 6c 69 | ,whi|ch impli| |00003e70| 65 73 20 75 2b 78 3d 77 | 2b 31 30 2a 6a 2c 20 69 |es u+x=w|+10*j, i| |00003e80| 6e 74 65 67 65 72 20 6a | 3e 3d 30 20 28 61 6e 64 |nteger j|>=0 (and| |00003e90| 20 6a 3c 3d 34 20 69 6e | 20 6f 75 72 20 63 61 73 | j<=4 in| our cas| |00003ea0| 65 29 0d 0d 74 68 75 73 | 20 77 65 20 68 61 76 65 |e)..thus| we have| |00003eb0| 20 78 3d 77 2d 75 2b 31 | 30 2a 6a 2c 20 30 3c 3d | x=w-u+1|0*j, 0<=| |00003ec0| 6a 3c 3d 34 20 6f 72 20 | 73 69 6d 70 6c 79 0d 0d |j<=4 or |simply..| |00003ed0| 76 3d 28 77 2d 75 2b 31 | 30 2a 6a 29 5e 73 70 65 |v=(w-u+1|0*j)^spe| |00003ee0| 63 69 61 6c 41 20 2c 20 | 6a 3d 30 2e 2e 34 20 73 |cialA , |j=0..4 s| |00003ef0| 75 63 68 20 74 68 61 74 | 20 76 3d 30 2e 2e 39 20 |uch that| v=0..9 | |00003f00| 6f 72 20 31 30 2e 2e 33 | 35 20 6f 72 20 30 2e 2e |or 10..3|5 or 0..| |00003f10| 33 35 0d 0d 62 75 74 20 | 62 65 69 6e 67 20 61 62 |35..but |being ab| |00003f20| 6c 65 20 74 6f 20 67 65 | 6e 65 72 61 6c 6c 79 20 |le to ge|nerally | |00003f30| 73 61 74 69 73 66 79 20 | 74 68 65 20 66 69 72 73 |satisfy |the firs| |00003f40| 74 20 72 61 6e 67 65 20 | 76 3d 30 2e 2e 39 20 72 |t range |v=0..9 r| |00003f50| 65 71 75 69 72 65 73 20 | 74 68 61 74 20 73 70 65 |equires |that spe| |00003f60| 63 69 61 6c 41 20 62 65 | 20 63 6f 6e 73 74 72 61 |cialA be| constra| |00003f70| 69 6e 65 64 20 74 6f 20 | 30 2e 2e 31 20 20 54 68 |ined to |0..1 Th| |00003f80| 69 73 20 72 61 6e 67 65 | 20 69 73 20 61 6c 73 6f |is range| is also| |00003f90| 20 73 75 66 66 69 63 69 | 65 6e 74 20 74 6f 20 67 | suffici|ent to g| |00003fa0| 75 61 72 61 6e 74 65 65 | 20 74 68 61 74 20 74 68 |uarantee| that th| |00003fb0| 65 20 6f 74 68 65 72 20 | 72 61 6e 67 65 73 20 6f |e other |ranges o| |00003fc0| 66 20 76 20 61 72 65 20 | 73 61 74 69 73 66 69 65 |f v are |satisfie| |00003fd0| 64 20 62 79 20 73 6f 6d | 65 20 76 61 6c 75 65 20 |d by som|e value | |00003fe0| 6f 66 20 6a 20 69 6e 20 | 30 2e 2e 34 0d 0d 53 74 |of j in |0..4..St| |00003ff0| 65 70 0d 3d 3d 3d 3d 0d | 0d 23 31 20 20 43 68 6f |ep.====.|.#1 Cho| |00004000| 6f 73 65 20 61 20 6c 65 | 6e 20 73 75 63 68 20 74 |ose a le|n such t| |00004010| 68 61 74 20 6c 65 6e 3e | 3d 6d 69 6e 4c 65 6e 67 |hat len>|=minLeng| |00004020| 74 68 2c 20 69 66 20 6c | 65 6e 25 32 3d 31 20 74 |th, if l|en%2=1 t| |00004030| 68 65 6e 20 53 4e 53 74 | 72 5b 6c 65 6e 2d 33 5d |hen SNSt|r[len-3]| |00004040| 20 63 61 6e 20 62 65 20 | 61 6e 79 20 63 68 61 72 | can be |any char| |00004050| 61 63 74 65 72 2e 0d 23 | 32 09 43 68 6f 6f 73 65 |acter..#|2.Choose| |00004060| 20 74 68 65 20 6c 61 73 | 74 20 74 77 6f 20 63 68 | the las|t two ch| |00004070| 61 72 61 63 74 65 72 73 | 20 2d 20 74 68 65 20 6c |aracters| - the l| |00004080| 61 73 74 20 63 68 61 72 | 61 63 74 65 72 20 6d 75 |ast char|acter mu| |00004090| 73 74 20 62 65 20 27 30 | 27 2e 2e 27 39 27 2c 27 |st be '0|'..'9','| |000040a0| 41 27 2e 2e 27 56 27 0d | 20 20 20 28 6e 6f 74 65 |A'..'V'.| (note| |000040b0| 20 79 6f 75 20 63 61 6e | 20 64 6f 20 74 68 69 73 | you can| do this| |000040c0| 20 69 6e 20 6d 61 6e 79 | 20 77 61 79 73 20 61 6e | in many| ways an| |000040d0| 64 20 73 74 69 6c 6c 20 | 67 65 74 20 74 68 65 20 |d still |get the | |000040e0| 76 61 6c 75 65 20 66 6f | 72 20 6d 79 56 61 6c 28 |value fo|r myVal(| |000040f0| 53 4e 53 74 72 5b 6c 65 | 6e 2d 31 5d 29 29 0d 23 |SNStr[le|n-1])).#| |00004100| 33 20 20 43 68 6f 6f 73 | 65 20 74 68 65 20 65 61 |3 Choos|e the ea| |00004110| 63 68 20 6f 66 20 74 68 | 65 20 66 69 72 73 74 20 |ch of th|e first | |00004120| 73 69 78 20 63 68 61 72 | 61 63 74 65 72 20 66 72 |six char|acter fr| |00004130| 6f 6d 20 27 30 27 2e 2e | 27 39 27 2c 27 41 27 2e |om '0'..|'9','A'.| |00004140| 2e 27 5a 27 20 77 69 74 | 68 20 74 68 65 20 63 6f |.'Z' wit|h the co| |00004150| 6e 73 74 72 61 69 6e 74 | 20 74 68 61 74 20 74 68 |nstraint| that th| |00004160| 65 0d 20 20 20 20 63 68 | 61 72 61 63 74 65 72 73 |e. ch|aracters| |00004170| 20 61 74 20 69 6e 64 65 | 78 65 73 20 32 2c 33 20 | at inde|xes 2,3 | |00004180| 61 6e 64 20 35 20 61 72 | 65 20 65 69 74 68 65 72 |and 5 ar|e either| |00004190| 20 61 6c 6c 20 64 69 67 | 69 74 73 20 6f 72 20 61 | all dig|its or a| |000041a0| 6c 6c 20 61 6c 70 68 61 | 27 73 2e 0d 23 34 09 43 |ll alpha|'s..#4.C| |000041b0| 61 6c 63 75 6c 61 74 65 | 20 74 68 65 20 63 6f 6e |alculate| the con| |000041c0| 73 74 61 6e 74 20 20 20 | 20 20 20 20 20 20 73 70 |stant | sp| |000041d0| 65 63 69 61 6c 41 3d 20 | 20 6d 79 56 61 6c 28 53 |ecialA= | myVal(S| |000041e0| 4e 53 74 72 5b 6c 65 6e | 5d 29 0d 23 35 09 43 61 |NStr[len|]).#5.Ca| |000041f0| 6c 63 75 6c 61 74 65 20 | 74 68 65 20 69 6e 69 74 |lculate |the init| |00004200| 69 61 6c 20 76 61 6c 75 | 65 20 6f 66 20 73 70 65 |ial valu|e of spe| |00004210| 63 69 61 6c 42 3d 28 28 | 6d 79 56 61 6c 28 53 4e |cialB=((|myVal(SN| |00004220| 53 74 72 5b 6c 65 6e 2d | 31 5d 29 5e 73 70 65 63 |Str[len-|1])^spec| |00004230| 69 61 6c 41 29 2b 6d 69 | 64 29 25 31 30 0d 23 36 |ialA)+mi|d)%10.#6| |00004240| 09 53 65 74 20 69 3d 30 | 0d 23 41 09 20 20 49 6e |.Set i=0|.#A. In| |00004250| 63 72 65 6d 65 6e 74 20 | 69 20 74 68 65 6e 20 73 |crement |i then s| |00004260| 65 74 20 6b 3d 6d 69 64 | 2d 69 0d 23 42 09 20 20 |et k=mid|-i.#B. | |00004270| 43 61 6c 63 75 6c 61 74 | 65 20 73 70 65 63 69 61 |Calculat|e specia| |00004280| 6c 43 3d 28 6d 79 56 61 | 6c 28 53 4e 53 74 72 5b |lC=(myVa|l(SNStr[| |00004290| 32 2a 69 5d 29 5e 73 70 | 65 63 69 61 6c 41 29 25 |2*i])^sp|ecialA)%| |000042a0| 31 30 0d 23 43 09 20 20 | 44 52 20 28 64 65 73 69 |10.#C. |DR (desi| |000042b0| 72 65 64 20 72 61 6e 67 | 65 29 20 3d 20 72 61 6e |red rang|e) = ran| |000042c0| 67 65 4f 66 54 79 70 65 | 28 53 4e 53 74 72 5b 6b |geOfType|(SNStr[k| |000042d0| 5d 29 20 3d 20 31 30 2e | 2e 33 35 20 69 66 20 69 |]) = 10.|.35 if i| |000042e0| 73 41 6c 70 68 61 28 53 | 4e 53 74 72 5b 6b 5d 29 |sAlpha(S|NStr[k])| |000042f0| 20 65 6c 73 65 20 3d 30 | 2e 2e 39 0d 23 44 09 20 | else =0|..9.#D. | |00004300| 20 53 6f 6c 76 65 20 73 | 70 65 63 69 61 6c 43 3d | Solve s|pecialC=| |00004310| 28 28 76 5e 73 70 65 63 | 69 61 6c 41 29 2b 6b 2b |((v^spec|ialA)+k+| |00004320| 73 70 65 63 69 61 6c 42 | 2b 28 69 2a 6d 75 6c 74 |specialB|+(i*mult| |00004330| 29 29 25 31 30 20 66 6f | 72 20 76 20 69 6e 20 44 |))%10 fo|r v in D| |00004340| 52 2e 0d 0d 20 20 20 20 | 20 20 6c 65 74 20 75 3d |R... | let u=| |00004350| 28 6b 2b 73 70 65 63 69 | 61 6c 42 2b 28 69 2a 6d |(k+speci|alB+(i*m| |00004360| 75 6c 74 29 29 25 31 30 | 20 74 68 65 6e 20 77 65 |ult))%10| then we| |00004370| 20 63 61 6e 20 72 65 77 | 72 69 74 65 20 74 68 65 | can rew|rite the| |00004380| 20 61 62 6f 76 65 20 61 | 73 0d 0d 20 20 20 20 20 | above a|s.. | |00004390| 20 28 75 2b 28 76 5e 73 | 70 65 63 69 61 6c 41 29 | (u+(v^s|pecialA)| |000043a0| 29 25 31 30 3d 73 70 65 | 63 69 61 6c 43 2c 20 76 |)%10=spe|cialC, v| |000043b0| 20 69 6e 20 44 52 2e 0d | 0d 20 20 20 20 20 20 54 | in DR..|. T| |000043c0| 68 61 74 20 69 73 3a 0d | 0d 20 20 20 20 20 20 76 |hat is:.|. v| |000043d0| 3d 28 73 70 65 63 69 61 | 6c 43 2d 75 2b 31 30 2a |=(specia|lC-u+10*| |000043e0| 6a 29 5e 73 70 65 63 69 | 61 6c 41 2c 20 66 6f 72 |j)^speci|alA, for| |000043f0| 20 61 6e 79 20 6a 3d 30 | 2e 2e 34 20 73 75 63 68 | any j=0|..4 such| |00004400| 20 74 68 61 74 20 73 70 | 65 63 69 61 6c 43 2d 75 | that sp|ecialC-u| |00004410| 2b 31 30 2a 6a 3e 3d 30 | 20 61 6e 64 20 76 20 69 |+10*j>=0| and v i| |00004420| 6e 20 44 52 2e 0d 0d 09 | 20 20 69 65 20 28 69 6e |n DR....| ie (in| |00004430| 20 70 73 65 75 64 6f 20 | 63 6f 64 65 29 3a 0d 0d | pseudo |code):..| |00004440| 09 20 20 6a 3d 30 0d 09 | 20 20 69 66 20 28 28 73 |. j=0..| if ((s| |00004450| 70 65 63 69 61 6c 43 2d | 75 29 3c 30 29 20 69 6e |pecialC-|u)<0) in| |00004460| 63 72 65 6d 65 6e 74 20 | 6a 0d 09 20 20 72 65 70 |crement |j.. rep| |00004470| 65 61 74 0d 09 20 20 20 | 20 63 61 6c 63 75 6c 61 |eat.. | calcula| |00004480| 74 65 20 76 3d 28 73 70 | 65 63 69 61 6c 43 2d 75 |te v=(sp|ecialC-u| |00004490| 2b 31 30 2a 6a 29 5e 73 | 70 65 63 69 61 6c 41 0d |+10*j)^s|pecialA.| |000044a0| 09 20 20 20 20 69 6e 63 | 72 65 6d 65 6e 74 20 6a |. inc|rement j| |000044b0| 0d 09 20 20 75 6e 74 69 | 6c 20 28 76 20 69 6e 20 |.. unti|l (v in | |000044c0| 44 52 29 0d 0d 23 45 20 | 20 20 20 53 65 74 20 53 |DR)..#E | Set S| |000044d0| 4e 53 74 72 5b 32 2a 6b | 2d 31 5d 3d 6d 79 56 61 |NStr[2*k|-1]=myVa| |000044e0| 6c 54 6f 43 68 61 72 28 | 76 29 20 61 6e 64 20 73 |lToChar(|v) and s| |000044f0| 70 65 63 69 61 6c 42 3d | 73 70 65 63 69 61 6c 43 |pecialB=|specialC| |00004500| 0d 23 46 20 20 20 20 69 | 66 20 28 69 3c 3d 28 28 |.#F i|f (i<=((| |00004510| 6d 69 64 2d 31 29 2f 32 | 29 29 20 67 6f 74 6f 20 |mid-1)/2|)) goto | |00004520| 73 74 65 70 23 41 0d 0d | 23 47 09 20 20 49 6e 63 |step#A..|#G. Inc| |00004530| 72 65 6d 65 6e 74 20 69 | 20 74 68 65 6e 20 73 65 |rement i| then se| |00004540| 74 20 6b 3d 6d 69 64 2d | 69 0d 23 48 20 20 20 20 |t k=mid-|i.#H | |00004550| 69 66 20 28 69 73 41 6c | 70 68 61 28 53 4e 53 74 |if (isAl|pha(SNSt| |00004560| 72 5b 6b 5d 29 29 0d 20 | 20 20 20 20 20 09 43 61 |r[k])). | .Ca| |00004570| 6c 63 75 6c 61 74 65 20 | 73 70 65 63 69 61 6c 42 |lculate |specialB| |00004580| 3d 28 28 28 53 4e 53 74 | 72 5b 32 2a 6b 2d 31 5d |=(((SNSt|r[2*k-1]| |00004590| 2d 27 41 27 29 5e 73 70 | 65 63 69 61 6c 41 29 2b |-'A')^sp|ecialA)+| |000045a0| 6b 2b 73 70 65 63 69 61 | 6c 42 2b 28 69 2a 6d 75 |k+specia|lB+(i*mu| |000045b0| 6c 74 29 29 25 31 30 0d | 20 20 20 20 20 20 65 6c |lt))%10.| el| |000045c0| 73 65 0d 20 20 20 20 20 | 20 09 43 61 6c 63 75 6c |se. | .Calcul| |000045d0| 61 74 65 20 73 70 65 63 | 69 61 6c 42 3d 28 28 28 |ate spec|ialB=(((| |000045e0| 53 4e 53 74 72 5b 32 2a | 6b 2d 31 5d 2d 27 30 27 |SNStr[2*|k-1]-'0'| |000045f0| 29 5e 73 70 65 63 69 61 | 6c 41 29 2b 6b 2b 73 70 |)^specia|lA)+k+sp| |00004600| 65 63 69 61 6c 42 2b 28 | 69 2a 6d 75 6c 74 29 29 |ecialB+(|i*mult))| |00004610| 25 31 30 0d 23 49 20 20 | 20 20 53 6f 6c 76 65 20 |%10.#I | Solve | |00004620| 73 70 65 63 69 61 6c 42 | 3d 28 28 76 5e 73 70 65 |specialB|=((v^spe| |00004630| 63 69 61 6c 41 29 25 31 | 30 20 66 6f 72 20 76 20 |cialA)%1|0 for v | |00004640| 69 6e 20 30 2e 2e 33 35 | 0d 0d 09 20 20 54 68 61 |in 0..35|... Tha| |00004650| 74 20 69 73 3a 0d 0d 09 | 20 20 76 3d 28 73 70 65 |t is:...| v=(spe| |00004660| 63 69 61 6c 42 2b 31 30 | 2a 6a 29 5e 73 70 65 63 |cialB+10|*j)^spec| |00004670| 69 61 6c 41 20 73 75 63 | 68 20 74 68 61 74 20 6a |ialA suc|h that j| |00004680| 20 69 6e 20 30 2e 2e 34 | 20 61 6e 64 20 76 20 69 | in 0..4| and v i| |00004690| 6e 20 30 2e 2e 33 35 0d | 0d 09 20 20 69 65 20 28 |n 0..35.|.. ie (| |000046a0| 69 6e 20 70 73 65 75 64 | 6f 20 63 6f 64 65 29 3a |in pseud|o code):| |000046b0| 0d 0d 09 20 20 6a 3d 30 | 0d 09 20 20 72 65 70 65 |... j=0|.. repe| |000046c0| 61 74 0d 09 20 20 20 20 | 63 61 6c 63 75 6c 61 74 |at.. |calculat| |000046d0| 65 20 76 3d 28 73 70 65 | 63 69 61 6c 42 2b 31 30 |e v=(spe|cialB+10| |000046e0| 2a 6a 29 5e 73 70 65 63 | 69 61 6c 41 0d 09 20 20 |*j)^spec|ialA.. | |000046f0| 20 20 69 6e 63 72 65 6d | 65 6e 74 20 6a 0d 09 20 | increm|ent j.. | |00004700| 20 75 6e 74 69 6c 20 28 | 6a 3d 35 29 0d 20 20 20 | until (|j=5). | |00004710| 70 69 63 6b 20 61 20 76 | 61 6c 69 64 20 76 61 6c |pick a v|alid val| |00004720| 75 65 20 6f 66 20 76 20 | 66 72 6f 6d 20 74 68 65 |ue of v |from the| |00004730| 20 76 61 6c 75 65 73 20 | 6a 75 73 74 20 63 61 6c | values |just cal| |00004740| 63 75 6c 61 74 65 64 0d | 0d 23 4a 20 20 20 20 69 |culated.|.#J i| |00004750| 66 20 28 69 3c 28 6d 69 | 64 2d 31 29 29 20 67 6f |f (i<(mi|d-1)) go| |00004760| 74 6f 20 73 74 65 70 23 | 47 0d 0d 45 58 3a 20 20 |to step#|G..EX: | |00004770| 46 6f 72 20 34 44 20 69 | 6e 73 69 64 65 72 20 31 |For 4D i|nsider 1| |00004780| 2e 30 2e 31 20 63 68 6f | 6f 73 69 6e 67 20 74 68 |.0.1 cho|osing th| |00004790| 65 20 69 6e 69 74 69 61 | 6c 20 76 61 6c 75 65 73 |e initia|l values| |000047a0| 20 53 4e 53 74 72 5b 5d | 3d 27 41 41 41 41 41 41 | SNStr[]|='AAAAAA| |000047b0| 3f 3f 3f 3f 3f 3f 35 30 | 27 20 6c 65 61 64 73 0d |??????50|' leads.| |000047c0| 74 6f 20 74 68 65 20 66 | 6f 6c 6c 6f 77 69 6e 67 |to the f|ollowing| |000047d0| 20 28 33 2a 34 2a 33 2a | 34 2a 32 2a 34 2a 34 29 | (3*4*3*|4*2*4*4)| |000047e0| 20 34 36 30 38 20 76 61 | 6c 69 64 20 73 65 72 69 | 4608 va|lid seri| |000047f0| 61 6c 20 6e 75 6d 62 65 | 72 73 2e 20 20 28 66 6f |al numbe|rs. (fo| |00004800| 72 20 61 6e 79 20 67 69 | 76 65 6e 20 53 4e 23 20 |r any gi|ven SN# | |00004810| 79 6f 75 20 6d 61 79 20 | 63 68 6f 6f 73 65 20 66 |you may |choose f| |00004820| 6f 72 20 65 61 63 68 20 | 69 6e 64 65 78 20 61 6e |or each |index an| |00004830| 79 20 6f 6e 65 20 6f 66 | 20 74 68 65 20 63 68 61 |y one of| the cha| |00004840| 72 61 63 74 65 72 73 20 | 69 6e 20 74 68 61 74 20 |racters |in that | |00004850| 69 6e 64 65 78 65 73 20 | 63 6f 6c 75 6d 6e 29 0d |indexes |column).| |00004860| 0d 53 4e 53 74 72 5b 5d | 3d 27 5c 70 41 41 41 41 |.SNStr[]|='\pAAAA| |00004870| 41 41 42 33 46 30 48 31 | 35 30 27 0d 20 20 20 20 |AAB3F0H1|50'. | |00004880| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 4c 44 50 | | LDP| |00004890| 41 52 42 46 0d 20 20 20 | 20 20 20 20 20 20 20 20 |ARBF. | | |000048a0| 20 20 20 20 20 20 56 4e | 5a 4b 20 4c 50 0d 20 20 | VN|ZK LP. | |000048b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | | |000048c0| 58 20 55 20 56 5a 0d 0d | 74 68 75 73 20 73 6f 6d |X U VZ..|thus som| |000048d0| 65 20 73 65 72 69 61 6c | 20 6e 75 6d 62 65 72 73 |e serial| numbers| |000048e0| 20 77 6f 75 6c 64 20 62 | 65 3a 0d 0d 27 41 41 41 | would b|e:..'AAA| |000048f0| 41 41 41 42 44 5a 55 52 | 31 46 30 27 0d 27 41 41 |AAABDZUR|1F0'.'AA| |00004900| 41 41 41 41 42 33 46 30 | 48 31 35 30 27 0d 27 41 |AAAAB3F0|H150'.'A| |00004910| 41 41 41 41 41 42 33 5a | 41 52 42 5a 30 27 0d 0d |AAAAAB3Z|ARBZ0'..| |00004920| 49 6e 20 66 61 63 74 20 | 69 66 20 77 65 20 6d 61 |In fact |if we ma| |00004930| 64 65 20 74 68 65 20 53 | 4e 23 20 31 35 20 63 68 |de the S|N# 15 ch| |00004940| 61 72 61 63 74 65 72 73 | 20 6c 6f 6e 67 20 77 65 |aracters| long we| |00004950| 20 63 6f 75 6c 64 20 61 | 72 62 69 74 72 61 72 69 | could a|rbitrari| |00004960| 6c 79 20 63 68 6f 6f 73 | 65 20 74 68 65 20 31 33 |ly choos|e the 13| |00004970| 74 68 20 63 68 61 72 61 | 63 74 65 72 20 61 6e 64 |th chara|cter and| |00004980| 20 67 65 74 20 61 74 20 | 6c 65 61 73 74 20 34 36 | get at |least 46| |00004990| 30 38 2a 33 36 3d 31 36 | 35 38 38 38 20 76 61 6c |08*36=16|5888 val| |000049a0| 69 64 20 73 65 72 69 61 | 6c 20 6e 75 6d 62 65 72 |id seria|l number| |000049b0| 73 20 74 68 61 74 20 61 | 6c 6c 20 62 65 67 61 6e |s that a|ll began| |000049c0| 20 77 69 74 68 20 27 41 | 41 41 41 41 41 27 20 61 | with 'A|AAAAA' a| |000049d0| 6e 64 20 65 6e 64 65 64 | 20 77 69 74 68 20 27 30 |nd ended| with '0| |000049e0| 27 20 21 21 21 20 28 61 | 63 74 75 61 6c 6c 79 20 |' !!! 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73 20 |ng will |work as | |00005370| 61 20 73 65 72 69 61 6c | 20 6e 75 6d 62 65 72 20 |a serial| number | |00005380| 77 68 65 6e 20 72 75 6e | 6e 69 6e 67 20 74 68 65 |when run|ning the| |00005390| 20 49 6e 73 74 61 6c 6c | 65 72 20 70 72 6f 67 72 | Install|er progr| |000053a0| 61 6d 20 2d 20 79 6f 75 | 20 63 61 6e 6e 6f 74 20 |am - you| cannot | |000053b0| 6a 75 73 74 20 64 72 61 | 67 20 74 68 65 20 63 6f |just dra|g the co| |000053c0| 6e 74 72 6f 6c 20 70 61 | 6e 65 6c 20 69 6e 74 6f |ntrol pa|nel into| |000053d0| 20 79 6f 75 72 20 53 79 | 73 74 65 6d 20 46 6f 6c | your Sy|stem Fol| |000053e0| 64 65 72 2e 20 54 68 65 | 20 4e 61 6d 65 2c 20 4f |der. 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