home *** CD-ROM | disk | FTP | other *** search
| MacBinary | 1998-08-28 | 2.0 MB | [SNKR/KRAK] |
open in: 
MacOS 8.1
|
Win98
|
DOS
view JSON data
|
view as text
This file was processed as: MacBinary
(archive/macBinary).
You can browse this item here: C&N 1998.08 Hacker Girlz
| Confidence | Program | Detection | Match Type | Support
|
|---|
| 10%
| dexvert
| MacBinary (archive/macBinary)
| fallback
| Supported |
| 100%
| file
| MacBinary II, inited, Fri Aug 28 06:24:01 1998, modified Fri Aug 28 06:31:52 1998, creator 'KRAK', type 'SNKR', 2048564 bytes "C&N 1998.08 Hacker Girlz" , at 0x1f42b4 286 bytes resource
| default (weak)
| |
| 99%
| file
| data
| default
| |
| 100%
| TrID
| MacBinary 2
| default (weak)
| |
| 100%
| dexmagic
| Picasso 64 Image
| 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 18 43 26 4e 20 31 39 | 39 38 2e 30 38 20 48 61 |..C&N 19|98.08 Ha|
|00000010| 63 6b 65 72 20 47 69 72 | 6c 7a 00 00 00 00 00 00 |cker Gir|lz......|
|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 1f 42 34 00 | 00 01 1e b2 0c 35 c1 b2 |.....B4.|.....5..|
|00000060| 0c 37 98 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |.7......|........|
|00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 b0 a8 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 32 32 37 34 0d | 30 38 2f 32 38 2f 39 38 |.2.2274.|08/28/98|
|000000a0| 0d 2d 0d 30 31 30 20 a5 | a5 a5 20 43 72 61 63 6b |.-.010 .|.. Crack|
|000000b0| 73 20 26 20 4e 75 6d 62 | 65 72 73 20 20 a5 a5 a5 |s & Numb|ers ...|
|000000c0| 20 30 31 30 0d 76 a5 0d | a0 a5 a5 a5 20 a5 20 a5 | 010.v..|.... . .|
|000000d0| a5 a5 0d 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|000000e0| 20 20 20 20 20 43 72 61 | 63 6b 73 20 26 20 4e 75 | Cra|cks & Nu|
|000000f0| 6d 62 65 72 73 20 27 39 | 38 0d 0d 20 20 20 20 20 |mbers '9|8.. |
|00000100| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 43 30 30 | | C00|
|00000110| 30 30 30 30 30 30 30 30 | 30 32 33 31 35 0d 2d 0d |00000000|02315.-.|
|00000120| 31 73 74 20 42 61 73 65 | 0d 76 31 2e 30 20 43 72 |1st Base|.v1.0 Cr|
|00000130| 61 63 6b 3a 0d a0 a5 a5 | a5 20 31 2e 30 20 43 72 |ack:....|. 1.0 Cr|
|00000140| 61 63 6b 3a 20 a5 a5 a5 | 0d 4d 6f 76 65 20 74 6f |ack: ...|.Move to|
|00000150| 20 62 6c 6f 63 6b 20 30 | 32 33 32 2c 20 70 6f 73 | block 0|232, pos|
|00000160| 69 74 69 6f 6e 20 30 30 | 36 46 2c 20 61 6e 64 20 |ition 00|6F, and |
|00000170| 63 68 61 6e 67 65 20 74 | 6f 20 30 31 0d 4d 6f 76 |change t|o 01.Mov|
|00000180| 65 20 74 6f 20 62 6c 6f | 63 6b 20 30 30 30 35 2c |e to blo|ck 0005,|
|00000190| 20 70 6f 73 69 74 69 6f | 6e 20 30 30 38 43 2c 20 | positio|n 008C, |
|000001a0| 61 6e 64 20 63 68 61 6e | 67 65 20 74 6f 20 30 31 |and chan|ge to 01|
|000001b0| 0d 4d 6f 76 65 20 74 6f | 20 62 6c 6f 63 6b 20 30 |.Move to| block 0|
|000001c0| 32 33 33 2c 20 70 6f 73 | 69 74 69 6f 6e 20 30 31 |233, pos|ition 01|
|000001d0| 39 46 2c 20 61 6e 64 20 | 63 68 61 6e 67 65 20 74 |9F, and |change t|
|000001e0| 6f 20 36 30 0d 4d 6f 76 | 65 20 74 6f 20 62 6c 6f |o 60.Mov|e to blo|
|000001f0| 63 6b 20 30 32 33 33 2c | 20 70 6f 73 69 74 69 6f |ck 0233,| positio|
|00000200| 6e 20 30 31 42 33 2c 20 | 61 6e 64 20 63 68 61 6e |n 01B3, |and chan|
|00000210| 67 65 20 74 6f 20 30 31 | 0d 4d 6f 76 65 20 74 6f |ge to 01|.Move to|
|00000220| 20 62 6c 6f 63 6b 20 30 | 32 33 33 2c 20 70 6f 73 | block 0|233, pos|
|00000230| 69 74 69 6f 6e 20 30 31 | 43 37 2c 20 61 6e 64 20 |ition 01|C7, and |
|00000240| 63 68 61 6e 67 65 20 74 | 6f 20 30 31 0d 4d 6f 76 |change t|o 01.Mov|
|00000250| 65 20 74 6f 20 62 6c 6f | 63 6b 20 30 30 30 35 2c |e to blo|ck 0005,|
|00000260| 20 70 6f 73 69 74 69 6f | 6e 20 30 30 38 32 2c 20 | positio|n 0082, |
|00000270| 61 6e 64 20 63 68 61 6e | 67 65 20 74 6f 20 38 30 |and chan|ge to 80|
|00000280| 0d 2d 0d 33 38 36 20 4d | 61 78 0d 76 37 2e 30 0d |.-.386 M|ax.v7.0.|
|00000290| 32 34 30 2d 31 30 34 33 | 34 33 0d 34 30 30 39 30 |240-1043|43.40090|
|000002a0| 32 30 36 30 30 32 0d 2d | 0d 33 44 20 53 74 75 64 |206002.-|.3D Stud|
|000002b0| 69 6f 20 4d 61 78 0d 76 | 32 2e 35 20 50 43 0d 53 |io Max.v|2.5 PC.S|
|000002c0| 65 72 69 61 6c 20 4e 75 | 6d 62 65 72 3a 20 36 36 |erial Nu|mber: 66|
|000002d0| 31 2d 39 33 38 34 32 37 | 36 32 20 20 20 20 20 4b |1-938427|62 K|
|000002e0| 65 79 3a 20 56 31 33 4d | 0d 43 6f 64 65 3a 20 31 |ey: V13M|.Code: 1|
|000002f0| 30 33 39 31 32 30 44 0d | 2d 0d 33 44 20 55 6c 74 |039120D.|-.3D Ult|
|00000300| 72 61 20 50 69 6e 62 61 | 6c 6c 0d 76 31 2e 30 20 |ra Pinba|ll.v1.0 |
|00000310| 43 72 61 63 6b 3a 0d 76 | a5 20 43 68 65 61 74 0d |Crack:.v|. Cheat.|
|00000320| a0 a5 a5 a5 20 31 2e 30 | 20 43 72 61 63 6b 3a 20 |.... 1.0| Crack: |
|00000330| a5 a5 a5 0d 33 44 20 55 | 6c 74 72 61 20 50 69 6e |....3D U|ltra Pin|
|00000340| 62 61 6c 6c 20 69 73 20 | 61 20 76 65 72 79 20 65 |ball is |a very e|
|00000350| 61 73 79 20 67 61 6d 65 | 20 74 6f 20 6b 72 61 6b |asy game| to krak|
|00000360| 2e 2e 0d 43 72 61 63 6b | 20 23 31 29 20 48 65 72 |...Crack| #1) Her|
|00000370| 65 20 69 73 20 77 68 61 | 74 20 79 6f 75 20 64 6f |e is wha|t you do|
|00000380| 3a 0d 0d 4f 70 65 6e 20 | 75 70 20 74 68 65 20 67 |:..Open |up the g|
|00000390| 61 6d 65 20 77 69 74 68 | 20 52 65 73 45 64 69 74 |ame with| ResEdit|
|000003a0| 20 61 6e 64 20 67 6f 20 | 74 6f 20 53 74 72 69 6e | and go |to Strin|
|000003b0| 67 73 0d 44 6f 75 62 6c | 65 20 63 6c 69 63 6b 20 |gs.Doubl|e click |
|000003c0| 6f 6e 20 22 41 70 70 20 | 53 70 65 63 69 66 69 63 |on "App |Specific|
|000003d0| 20 53 74 72 69 6e 67 22 | 0d 47 6f 20 74 6f 20 73 | String"|.Go to s|
|000003e0| 74 72 69 6e 67 20 23 32 | 20 61 6e 64 20 65 72 61 |tring #2| and era|
|000003f0| 73 65 20 74 68 65 20 6c | 69 6e 65 20 74 68 61 74 |se the l|ine that|
|00000400| 20 73 61 79 73 20 22 33 | 44 20 55 6c 74 72 61 20 | says "3|D Ultra |
|00000410| 50 69 6e 62 61 6c 6c 20 | 43 44 22 0d 53 61 76 65 |Pinball |CD".Save|
|00000420| 20 63 68 61 6e 67 65 73 | 20 61 6e 64 20 70 6c 61 | changes| and pla|
|00000430| 79 2e 2e 2e 0d 0d 43 72 | 61 63 6b 20 23 32 29 20 |y.....Cr|ack #2) |
|00000440| 54 6f 20 67 65 74 20 33 | 44 20 55 6c 74 72 61 20 |To get 3|D Ultra |
|00000450| 50 69 6e 62 61 6c 6c 20 | 74 6f 20 72 75 6e 20 77 |Pinball |to run w|
|00000460| 69 74 68 6f 75 74 20 74 | 68 65 20 43 44 20 69 73 |ithout t|he CD is|
|00000470| 20 72 65 61 6c 20 65 61 | 73 79 2e 0d 0d 4f 70 65 | real ea|sy...Ope|
|00000480| 6e 20 74 68 65 20 6d 61 | 69 6e 20 61 70 70 20 77 |n the ma|in app w|
|00000490| 69 74 68 20 52 65 73 45 | 64 69 74 2c 0d 67 6f 20 |ith ResE|dit,.go |
|000004a0| 74 6f 20 53 54 52 23 20 | 38 30 33 20 22 41 70 70 |to STR# |803 "App|
|000004b0| 20 53 70 65 63 69 66 69 | 63 20 53 74 72 69 6e 67 | Specifi|c String|
|000004c0| 73 22 2c 0d 73 74 72 69 | 6e 67 20 23 32 20 73 61 |s",.stri|ng #2 sa|
|000004d0| 79 73 20 22 33 44 20 55 | 6c 74 72 61 20 50 69 6e |ys "3D U|ltra Pin|
|000004e0| 62 61 6c 6c 20 43 44 22 | 2c 0d 63 68 61 6e 67 65 |ball CD"|,.change|
|000004f0| 20 69 74 20 74 6f 20 22 | 3a 22 2c 0d 74 68 61 74 | it to "|:",.that|
|00000500| 73 20 61 20 63 6f 6c 6f | 6e 20 77 69 74 68 6f 75 |s a colo|n withou|
|00000510| 74 20 74 68 65 20 71 75 | 6f 74 65 73 0d 0d 4e 6f |t the qu|otes..No|
|00000520| 77 20 69 74 27 6c 6c 20 | 72 75 6e 20 77 2f 6f 20 |w it'll |run w/o |
|00000530| 74 68 65 20 43 44 2e 0d | 0d a5 a5 a5 20 a5 20 43 |the CD..|.... . C|
|00000540| 68 65 61 74 20 a5 a5 a5 | 0d 31 20 2d 20 43 68 6f |heat ...|.1 - Cho|
|00000550| 6f 73 65 20 61 20 70 69 | 6e 62 61 6c 6c 20 74 61 |ose a pi|nball ta|
|00000560| 62 6c 65 20 61 6e 64 20 | 73 74 61 72 74 20 61 20 |ble and |start a |
|00000570| 6e 65 77 20 67 61 6d 65 | 2e 0d 32 20 2d 20 50 72 |new game|..2 - Pr|
|00000580| 65 73 73 20 3c 45 53 43 | 3e 20 61 6e 64 20 74 79 |ess <ESC|> and ty|
|00000590| 70 65 20 22 6b 65 72 6d | 69 74 22 20 28 77 69 74 |pe "kerm|it" (wit|
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|000005b0| 20 70 72 65 73 73 20 3c | 65 6e 74 65 72 3e 0d 33 | press <|enter>.3|
|000005c0| 20 2d 20 50 72 65 73 73 | 20 3c 45 53 43 3e 20 61 | - Press| <ESC> a|
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|000005e0| 68 65 20 66 6f 6c 6c 6f | 77 69 6e 67 20 63 6f 64 |he follo|wing cod|
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|00000610| 61 63 6b 20 2d 42 61 6c | 6c 20 6e 65 76 65 72 20 |ack -Bal|l never |
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|00000b20| 20 42 61 63 6b 75 70 0d | 76 36 2e 30 2e 78 0d 76 | Backup.|v6.0.x.v|
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|00000c10| 6f 64 65 3a 20 39 32 30 | 31 39 35 39 34 20 20 20 |ode: 920|19594 |
|00000c20| 20 20 20 20 20 20 20 4c | 69 63 65 6e 73 65 3a 20 | L|icense: |
|00000c30| 38 32 43 37 34 30 45 37 | 45 42 36 34 43 43 43 44 |82C740E7|EB64CCCD|
|00000c40| 0d 76 31 2e 32 0d 49 44 | 3a 20 37 33 34 35 39 39 |.v1.2.ID|: 734599|
|00000c50| 32 36 39 38 38 30 34 34 | 31 0d 43 6f 64 65 3a 20 |26988044|1.Code: |
|00000c60| 30 32 30 35 37 36 31 36 | 34 36 31 32 33 34 34 20 |02057616|4612344 |
|00000c70| 20 20 4c 69 63 65 6e 73 | 65 3a 20 32 33 35 34 35 | Licens|e: 23545|
|00000c80| 34 34 36 36 31 38 38 38 | 38 36 0d a0 a5 a5 a5 20 |44661888|86..... |
|00000c90| 36 2e 30 2e 78 20 a5 a5 | a5 0d 53 65 65 20 76 31 |6.0.x ..|..See v1|
|00000ca0| 2e 35 2e 78 0d 2d 0d 34 | 44 20 42 6f 78 69 6e 67 |.5.x.-.4|D Boxing|
|00000cb0| 0d 76 31 2e 30 20 43 72 | 61 63 6b 3a 0d 76 a5 20 |.v1.0 Cr|ack:.v. |
|00000cc0| 43 68 65 61 74 0d a0 a5 | a5 a5 20 31 2e 30 20 43 |Cheat...|.. 1.0 C|
|00000cd0| 72 61 63 6b 3a 20 a5 a5 | a5 0d 43 4f 44 45 20 31 |rack: ..|..CODE 1|
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|00002be0| 0d 50 61 72 74 69 61 6c | 20 43 72 61 63 6b 20 74 |.Partial| Crack t|
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|00002c60| 6e 20 74 68 65 20 63 6f | 70 79 3a 0d 20 20 20 20 |n the co|py:. |
|00002c70| 20 43 4f 44 45 20 33 31 | 2b 24 32 32 45 20 20 20 | CODE 31|+$22E |
|00002c80| 20 20 46 72 6f 6d 20 36 | 36 20 20 20 20 20 20 20 | From 6|6 |
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|00002d60| 20 44 65 6c 65 74 65 20 | 74 68 65 20 63 6f 70 79 | Delete |the copy|
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|00004230| 20 6e 6f 6e 2d 74 72 69 | 76 69 61 6c 0d 20 20 20 | non-tri|vial. |
|00004240| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 73 70 65 | | spe|
|00004250| 63 69 61 6c 42 3d 28 28 | 28 53 4e 53 74 72 5b 32 |cialB=((|(SNStr[2|
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|00004270| 65 63 69 61 6c 41 29 2b | 6b 2b 73 70 65 63 69 61 |ecialA)+|k+specia|
|00004280| 6c 42 2b 28 69 2a 6d 75 | 6c 74 29 29 25 31 30 3b |lB+(i*mu|lt))%10;|
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|000042b0| 20 20 73 70 65 63 69 61 | 6c 42 3d 28 28 28 53 4e | specia|lB=(((SN|
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|000042f0| 29 25 31 30 3b 0d 0d 20 | 20 20 20 20 20 20 20 20 |)%10;.. | |
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|00004320| 20 20 20 20 20 20 20 20 | 20 20 20 20 69 2b 2b 3b | | i++;|
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|00004360| 75 72 6e 20 69 73 56 61 | 6c 69 64 3b 0d 7d 0d 2f |urn isVa|lid;.}./|
|00004370| 2a 20 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |* ******|********|
|00004380| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00004390| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|000043a0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|000043b0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|000043c0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|000043d0| 20 2a 2f 0d 2f 2a 20 2a | 2a 2a 2a 2a 2a 2a 2a 2a | */./* *|********|
|000043e0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|000043f0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00004400| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00004410| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00004420| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00004430| 2a 2a 2a 2a 2a 20 2a 2f | 0d 2f 2a 20 2a 2a 2a 2a |***** */|./* ****|
|00004440| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00004450| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00004460| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
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|00004480| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00004490| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 20 2a 2f 0d 49 20 |********|** */.I |
|000044a0| 77 69 6c 6c 20 70 72 65 | 73 65 6e 74 20 74 77 6f |will pre|sent two|
|000044b0| 20 65 6e 74 69 72 65 6c | 79 20 64 69 66 66 65 72 | entirel|y differ|
|000044c0| 65 6e 74 20 6d 65 74 68 | 6f 64 73 20 66 6f 72 20 |ent meth|ods for |
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|000044e0| 6c 20 6e 75 6d 62 65 72 | 73 2e 20 20 54 68 65 20 |l number|s. The |
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|00004510| 61 74 74 61 63 6b 20 69 | 73 20 74 6f 20 72 65 73 |attack i|s to res|
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|00004530| 6d 20 64 6f 6d 61 69 6e | 20 74 6f 20 74 68 61 74 |m domain| to that|
|00004540| 20 6f 66 20 65 6e 74 69 | 72 65 6c 79 20 6e 75 6d | of enti|rely num|
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|00004560| 65 72 73 2e 20 20 54 68 | 69 73 20 61 70 70 72 6f |ers. Th|is appro|
|00004570| 61 63 68 20 72 65 6d 6f | 76 65 73 20 74 68 65 20 |ach remo|ves the |
|00004580| 64 69 66 66 69 63 75 6c | 74 79 20 69 6d 70 6f 73 |difficul|ty impos|
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|000045b0| 20 2d 20 62 75 74 20 69 | 6d 70 6f 73 65 73 20 74 | - but i|mposes t|
|000045c0| 68 65 20 6c 65 73 73 65 | 72 20 72 65 73 74 72 69 |he lesse|r restri|
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|000045e0| 5b 4c 65 6e 5d 20 69 73 | 20 27 30 27 20 6f 72 20 |[Len] is| '0' or |
|000045f0| 27 31 27 20 69 6e 20 67 | 65 6e 65 72 61 6c 20 28 |'1' in g|eneral (|
|00004600| 73 70 65 63 69 66 69 63 | 20 63 6f 75 6e 74 65 72 |specific| counter|
|00004610| 65 78 61 6d 70 6c 65 73 | 20 65 78 69 73 74 29 2e |examples| exist).|
|00004620| 20 20 54 68 75 73 20 77 | 65 20 63 61 6e 20 61 72 | Thus w|e can ar|
|00004630| 62 69 74 72 61 72 69 6c | 79 20 63 68 6f 6f 73 65 |bitraril|y choose|
|00004640| 20 64 69 67 69 74 73 20 | 66 6f 72 20 74 68 65 20 | digits |for the |
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|00004660| 64 20 69 6e 64 65 78 20 | 63 68 61 72 61 63 74 65 |d index |characte|
|00004670| 72 73 2c 20 74 68 65 20 | 32 6e 64 20 74 6f 20 6c |rs, the |2nd to l|
|00004680| 61 73 74 20 28 6c 65 6e | 2d 31 29 20 63 68 61 72 |ast (len|-1) char|
|00004690| 61 63 74 65 72 20 28 61 | 63 74 75 61 6c 6c 79 20 |acter (a|ctually |
|000046a0| 74 68 69 73 20 63 68 61 | 72 61 63 74 65 72 20 63 |this cha|racter c|
|000046b0| 61 6e 20 65 76 65 6e 20 | 62 65 20 61 6e 20 61 6c |an even |be an al|
|000046c0| 70 68 61 29 2c 20 77 68 | 69 6c 65 20 74 68 65 20 |pha), wh|ile the |
|000046d0| 6c 61 73 74 20 63 68 61 | 72 61 63 74 65 72 20 69 |last cha|racter i|
|000046e0| 73 20 63 68 6f 6f 73 65 | 6e 20 61 73 20 27 30 27 |s choose|n as '0'|
|000046f0| 20 6f 72 20 27 31 27 2e | 20 20 4f 6e 63 65 20 74 | or '1'.| Once t|
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|00004710| 65 20 62 65 65 6e 20 6d | 61 64 65 20 69 74 20 69 |e been m|ade it i|
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|00004760| 20 66 69 72 73 74 20 28 | 6d 69 64 2d 31 29 20 65 | first (|mid-1) e|
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|00004780| 63 20 63 68 61 72 61 63 | 74 65 72 73 2e 20 20 54 |c charac|ters. T|
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|000047b0| 0d 3d 3d 3d 3d 0d 0d 23 | 31 20 43 68 6f 6f 73 65 |.====..#|1 Choose|
|000047c0| 20 6c 65 6e 20 73 75 63 | 68 20 74 68 61 74 20 6c | len suc|h that l|
|000047d0| 65 6e 3e 3d 6d 69 6e 4c | 65 6e 67 74 68 20 61 6e |en>=minL|ength an|
|000047e0| 64 20 6c 65 6e 25 32 3d | 30 0d 23 32 20 53 65 74 |d len%2=|0.#2 Set|
|000047f0| 20 6d 69 64 3d 6c 65 6e | 2f 32 0d 23 33 20 43 68 | mid=len|/2.#3 Ch|
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|00004810| 72 61 63 74 65 72 73 20 | 74 6f 20 6f 63 63 75 70 |racters |to occup|
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|00004850| 0d 23 34 20 43 68 6f 6f | 73 65 20 6e 75 6d 65 72 |.#4 Choo|se numer|
|00004860| 69 63 20 6f 72 20 61 6c | 70 68 61 20 63 68 61 72 |ic or al|pha char|
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|00004880| 53 4e 53 74 72 5b 6c 65 | 6e 2d 31 5d 0d 23 35 20 |SNStr[le|n-1].#5 |
|00004890| 43 68 6f 6f 73 65 20 6e | 75 6d 65 72 69 63 20 63 |Choose n|umeric c|
|000048a0| 68 61 72 61 63 74 65 72 | 20 27 30 27 20 6f 72 20 |haracter| '0' or |
|000048b0| 27 31 27 20 74 6f 20 6f | 63 63 75 70 79 20 53 4e |'1' to o|ccupy SN|
|000048c0| 53 74 72 5b 6c 65 6e 5d | 0d 23 36 20 69 66 20 6c |Str[len]|.#6 if l|
|000048d0| 65 6e 25 32 3d 31 20 28 | 6c 65 6e 20 69 73 20 6f |en%2=1 (|len is o|
|000048e0| 64 64 29 20 74 68 65 6e | 20 63 68 6f 6f 73 65 20 |dd) then| choose |
|000048f0| 61 6e 20 61 72 62 69 74 | 72 61 72 79 20 63 68 61 |an arbit|rary cha|
|00004900| 72 61 63 74 65 72 20 66 | 6f 72 20 53 4e 53 74 72 |racter f|or SNStr|
|00004910| 5b 6c 65 6e 2d 33 5d 0d | 23 37 20 43 61 6c 63 75 |[len-3].|#7 Calcu|
|00004920| 6c 61 74 65 20 74 68 65 | 20 63 6f 6e 73 74 61 6e |late the| constan|
|00004930| 74 20 20 20 20 20 20 20 | 20 20 73 70 65 63 69 61 |t | specia|
|00004940| 6c 41 3d 20 20 6d 79 56 | 61 6c 28 53 4e 53 74 72 |lA= myV|al(SNStr|
|00004950| 5b 6c 65 6e 5d 29 0d 23 | 38 20 43 61 6c 63 75 6c |[len]).#|8 Calcul|
|00004960| 61 74 65 20 74 68 65 20 | 69 6e 69 74 69 61 6c 20 |ate the |initial |
|00004970| 76 61 6c 75 65 20 6f 66 | 20 73 70 65 63 69 61 6c |value of| special|
|00004980| 42 3d 28 28 6d 79 56 61 | 6c 28 53 4e 53 74 72 5b |B=((myVa|l(SNStr[|
|00004990| 6c 65 6e 2d 31 5d 29 5e | 73 70 65 63 69 61 6c 41 |len-1])^|specialA|
|000049a0| 29 2b 6d 69 64 29 25 31 | 30 0d 23 39 20 53 65 74 |)+mid)%1|0.#9 Set|
|000049b0| 20 69 3d 30 0d 23 41 20 | 20 20 49 6e 63 72 65 6d | i=0.#A | Increm|
|000049c0| 65 6e 74 20 69 20 74 68 | 65 6e 20 73 65 74 20 6b |ent i th|en set k|
|000049d0| 3d 6d 69 64 2d 69 0d 23 | 42 20 20 20 43 61 6c 63 |=mid-i.#|B Calc|
|000049e0| 75 6c 61 74 65 20 73 70 | 65 63 69 61 6c 42 3d 28 |ulate sp|ecialB=(|
|000049f0| 28 28 53 4e 53 74 72 5b | 32 2a 6b 2d 31 5d 2d 27 |((SNStr[|2*k-1]-'|
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|00004a10| 73 70 65 63 69 61 6c 42 | 2b 28 69 2a 6d 75 6c 74 |specialB|+(i*mult|
|00004a20| 29 29 25 31 30 0d 0d 20 | 20 20 20 20 41 74 20 74 |))%10.. | At t|
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|00004a40| 77 20 74 68 61 74 20 30 | 3c 3d 73 70 65 63 69 61 |w that 0|<=specia|
|00004a50| 6c 41 3c 32 20 61 6e 64 | 20 30 3c 3d 73 70 65 63 |lA<2 and| 0<=spec|
|00004a60| 69 61 6c 42 3c 31 30 0d | 20 20 20 20 20 57 65 20 |ialB<10.| We |
|00004a70| 6e 65 65 64 20 74 6f 20 | 66 69 6e 64 20 74 68 65 |need to |find the|
|00004a80| 20 76 61 6c 75 65 20 6f | 66 20 43 3d 6d 79 56 61 | value o|f C=myVa|
|00004a90| 6c 28 53 4e 53 74 72 5b | 32 2a 69 5d 29 20 73 75 |l(SNStr[|2*i]) su|
|00004aa0| 63 68 20 74 68 61 74 0d | 0d 20 20 20 20 20 28 43 |ch that.|. (C|
|00004ab0| 5e 73 70 65 63 69 61 6c | 41 29 25 31 30 3d 73 70 |^special|A)%10=sp|
|00004ac0| 65 63 69 61 6c 42 2c 20 | 43 3d 30 2e 2e 39 2e 0d |ecialB, |C=0..9..|
|00004ad0| 0d 20 20 20 20 20 4c 65 | 74 74 69 6e 67 20 44 3d |. Le|tting D=|
|00004ae0| 43 5e 73 70 65 63 69 61 | 6c 41 20 74 68 65 20 61 |C^specia|lA the a|
|00004af0| 62 6f 76 65 20 6d 6f 64 | 75 6c 61 72 20 65 71 75 |bove mod|ular equ|
|00004b00| 61 74 69 6f 6e 20 62 65 | 63 6f 6d 65 73 20 44 25 |ation be|comes D%|
|00004b10| 31 30 3d 73 70 65 63 69 | 61 6c 42 2c 20 43 3d 30 |10=speci|alB, C=0|
|00004b20| 2e 2e 39 0d 0d 20 20 20 | 20 20 54 68 65 20 67 65 |..9.. | The ge|
|00004b30| 6e 65 72 61 6c 20 73 6f | 6c 75 74 69 6f 6e 20 28 |neral so|lution (|
|00004b40| 74 68 65 20 65 71 75 61 | 74 69 6f 6e 20 68 61 73 |the equa|tion has|
|00004b50| 20 73 6f 6c 75 74 69 6f | 6e 73 20 73 69 6e 63 65 | solutio|ns since|
|00004b60| 20 73 70 65 63 69 61 6c | 42 3c 31 30 29 20 74 6f | special|B<10) to|
|00004b70| 20 74 68 69 73 20 6d 6f | 64 75 6c 61 72 20 65 71 | this mo|dular eq|
|00004b80| 75 61 74 69 6f 6e 0d 20 | 20 20 20 20 69 73 3a 0d |uation. | is:.|
|00004b90| 0d 20 20 20 20 20 44 3d | 73 70 65 63 69 61 6c 42 |. D=|specialB|
|00004ba0| 20 2b 20 31 30 2a 6d 2c | 20 69 6e 74 65 67 65 72 | + 10*m,| integer|
|00004bb0| 20 6d 3d 30 2e 2e 69 6e | 66 69 6e 69 74 79 2e 0d | m=0..in|finity..|
|00004bc0| 0d 20 20 20 20 20 48 6f | 77 65 76 65 72 20 73 69 |. Ho|wever si|
|00004bd0| 6e 63 65 20 77 65 20 6d | 75 73 74 20 68 61 76 65 |nce we m|ust have|
|00004be0| 20 43 3d 30 2e 2e 39 20 | 28 69 6e 20 6f 72 64 65 | C=0..9 |(in orde|
|00004bf0| 72 20 74 6f 20 67 65 74 | 20 61 20 6e 75 6d 65 72 |r to get| a numer|
|00004c00| 69 63 20 53 4e 23 29 20 | 61 6e 64 20 73 70 65 63 |ic SN#) |and spec|
|00004c10| 69 61 6c 41 3d 30 2e 2e | 31 20 77 65 20 6b 6e 6f |ialA=0..|1 we kno|
|00004c20| 77 0d 20 20 20 20 20 74 | 68 61 74 20 44 3d 30 2e |w. t|hat D=0.|
|00004c30| 2e 39 20 73 69 6e 63 65 | 20 44 3d 43 5e 73 70 65 |.9 since| D=C^spe|
|00004c40| 63 69 61 6c 41 20 61 6e | 64 20 39 5e 31 3d 38 3c |cialA an|d 9^1=8<|
|00004c50| 31 30 20 61 6e 64 20 61 | 2d 62 3c 3d 30 3c 3d 61 |10 and a|-b<=0<=a|
|00004c60| 5e 62 3c 3d 61 2b 62 20 | 2c 20 77 68 65 6e 20 30 |^b<=a+b |, when 0|
|00004c70| 3c 3d 62 3c 3d 61 0d 20 | 20 20 20 20 28 69 65 20 |<=b<=a. | (ie |
|00004c80| 44 3d 30 2e 2e 39 20 73 | 69 6e 63 65 20 30 2e 2e |D=0..9 s|ince 0..|
|00004c90| 39 20 78 6f 72 20 30 2e | 2e 31 3d 30 2e 2e 39 2c |9 xor 0.|.1=0..9,|
|00004ca0| 20 62 75 74 20 30 2e 2e | 39 20 78 6f 72 20 32 2e | but 0..|9 xor 2.|
|00004cb0| 2e 6d 3d 30 2e 2e 39 2b | 6d 20 2d 2d 20 74 68 69 |.m=0..9+|m -- thi|
|00004cc0| 73 20 69 73 20 74 68 65 | 20 72 65 61 73 6f 6e 20 |s is the| reason |
|00004cd0| 77 68 79 0d 20 20 20 20 | 20 73 70 65 63 69 61 6c |why. | special|
|00004ce0| 41 20 28 61 6e 64 20 74 | 68 75 73 20 74 68 65 20 |A (and t|hus the |
|00004cf0| 6c 61 73 74 20 63 68 61 | 72 61 63 74 65 72 29 20 |last cha|racter) |
|00004d00| 6d 75 73 74 20 62 65 20 | 72 65 73 74 72 69 63 74 |must be |restrict|
|00004d10| 65 64 20 74 6f 20 30 2e | 2e 31 29 0d 0d 20 20 20 |ed to 0.|.1).. |
|00004d20| 20 20 54 68 75 73 20 73 | 69 6e 63 65 20 77 65 20 | Thus s|ince we |
|00004d30| 6b 6e 6f 77 20 74 68 61 | 74 20 44 3d 30 2e 2e 39 |know tha|t D=0..9|
|00004d40| 20 77 65 20 63 61 6e 20 | 69 67 6e 6f 72 65 20 74 | we can |ignore t|
|00004d50| 68 65 20 6d 6f 64 20 6f | 70 65 72 61 74 6f 72 20 |he mod o|perator |
|00004d60| 61 6e 64 20 77 6f 72 6b | 20 77 69 74 68 20 74 68 |and work| with th|
|00004d70| 65 20 73 69 6d 70 6c 65 | 20 65 71 75 61 74 69 6f |e simple| equatio|
|00004d80| 6e 0d 0d 20 20 20 20 20 | 44 3d 73 70 65 63 69 61 |n.. |D=specia|
|00004d90| 6c 42 20 6f 72 20 43 5e | 73 70 65 63 69 61 6c 41 |lB or C^|specialA|
|00004da0| 3d 73 70 65 63 69 61 6c | 42 20 77 68 69 63 68 20 |=special|B which |
|00004db0| 69 6d 70 6c 69 65 73 20 | 43 3d 73 70 65 63 69 61 |implies |C=specia|
|00004dc0| 6c 42 5e 73 70 65 63 69 | 61 6c 41 20 74 68 75 73 |lB^speci|alA thus|
|00004dd0| 20 77 65 20 68 61 76 65 | 20 73 74 65 70 20 23 43 | we have| step #C|
|00004de0| 0d 0d 23 43 20 20 20 43 | 61 6c 63 75 6c 61 74 65 |..#C C|alculate|
|00004df0| 20 74 68 65 20 73 6f 6c | 75 74 69 6f 6e 20 63 68 | the sol|ution ch|
|00004e00| 61 72 61 63 74 65 72 20 | 61 73 20 53 4e 53 74 72 |aracter |as SNStr|
|00004e10| 5b 32 2a 69 5d 3d 6d 79 | 56 61 6c 54 6f 43 68 61 |[2*i]=my|ValToCha|
|00004e20| 72 28 73 70 65 63 69 61 | 6c 42 5e 73 70 65 63 69 |r(specia|lB^speci|
|00004e30| 61 6c 41 29 0d 23 44 20 | 20 20 69 66 20 28 69 3c |alA).#D | if (i<|
|00004e40| 6d 69 64 29 20 67 6f 74 | 6f 20 73 74 65 70 20 23 |mid) got|o step #|
|00004e50| 41 0d 0d 45 78 61 6d 70 | 6c 65 20 66 6f 72 20 6c |A..Examp|le for l|
|00004e60| 65 6e 3d 31 34 2c 20 6d | 75 6c 74 3d 39 0d 0d 43 |en=14, m|ult=9..C|
|00004e70| 68 61 72 20 20 20 20 20 | 20 30 30 30 30 30 30 30 |har | 0000000|
|00004e80| 30 30 30 31 31 31 31 31 | 0d 49 6e 64 65 78 20 20 |00011111|.Index |
|00004e90| 20 20 20 30 31 32 33 34 | 35 36 37 38 39 30 31 32 | 01234|56789012|
|00004ea0| 33 34 0d 20 20 20 20 20 | 20 20 20 20 20 2d 2d 2d |34. | ---|
|00004eb0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 0d 53 4e 53 |--------|----.SNS|
|00004ec0| 74 72 5b 5d 3d 22 5c 70 | 31 23 33 23 35 23 37 23 |tr[]="\p|1#3#5#7#|
|00004ed0| 39 23 31 23 39 31 22 0d | 0d 41 66 74 65 72 20 53 |9#1#91".|.After S|
|00004ee0| 74 65 70 20 41 0d 0d 6d | 69 64 3d 37 0d 73 70 65 |tep A..m|id=7.spe|
|00004ef0| 63 69 61 6c 41 3d 6d 79 | 56 61 6c 28 27 31 27 29 |cialA=my|Val('1')|
|00004f00| 3d 31 0d 73 70 65 63 69 | 61 6c 42 3d 28 28 39 5e |=1.speci|alB=((9^|
|00004f10| 31 29 2b 37 29 25 31 30 | 3d 28 38 2b 37 29 25 31 |1)+7)%10|=(8+7)%1|
|00004f20| 30 3d 35 0d 0d 41 66 74 | 65 72 20 53 74 65 70 20 |0=5..Aft|er Step |
|00004f30| 43 20 28 69 3d 31 2c 6b | 3d 36 29 0d 73 70 65 63 |C (i=1,k|=6).spec|
|00004f40| 69 61 6c 42 3d 28 28 28 | 27 31 27 2d 27 30 27 29 |ialB=(((|'1'-'0')|
|00004f50| 5e 31 29 2b 36 2b 35 2b | 39 29 25 31 30 3d 28 30 |^1)+6+5+|9)%10=(0|
|00004f60| 2b 32 30 29 25 31 30 3d | 31 30 25 31 30 3d 30 0d |+20)%10=|10%10=0.|
|00004f70| 53 4e 53 74 72 5b 32 5d | 3d 6d 79 56 61 6c 54 6f |SNStr[2]|=myValTo|
|00004f80| 43 68 61 72 28 30 5e 31 | 29 3d 27 31 27 0d 0d 41 |Char(0^1|)='1'..A|
|00004f90| 66 74 65 72 20 53 74 65 | 70 20 43 20 28 69 3d 32 |fter Ste|p C (i=2|
|00004fa0| 2c 6b 3d 35 29 0d 73 70 | 65 63 69 61 6c 42 3d 28 |,k=5).sp|ecialB=(|
|00004fb0| 28 28 27 39 27 2d 27 30 | 27 29 5e 31 29 2b 35 2b |(('9'-'0|')^1)+5+|
|00004fc0| 30 2b 38 29 25 31 30 3d | 28 28 39 5e 31 29 2b 31 |0+8)%10=|((9^1)+1|
|00004fd0| 33 29 25 31 30 3d 32 31 | 25 31 30 3d 31 20 2f 2f |3)%10=21|%10=1 //|
|00004fe0| 38 20 69 73 20 6a 75 73 | 74 20 31 38 25 31 30 20 |8 is jus|t 18%10 |
|00004ff0| 28 6d 6f 64 75 6c 61 72 | 20 73 69 6d 70 6c 69 66 |(modular| simplif|
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|00005010| 5d 3d 6d 79 56 61 6c 54 | 6f 43 68 61 72 28 31 5e |]=myValT|oChar(1^|
|00005020| 31 29 3d 27 30 27 0d 0d | 41 66 74 65 72 20 53 74 |1)='0'..|After St|
|00005030| 65 70 20 43 20 28 69 3d | 33 2c 6b 3d 34 29 0d 73 |ep C (i=|3,k=4).s|
|00005040| 70 65 63 69 61 6c 42 3d | 28 28 28 27 37 27 2d 27 |pecialB=|((('7'-'|
|00005050| 30 27 29 5e 31 29 2b 34 | 2b 31 2b 37 29 25 31 30 |0')^1)+4|+1+7)%10|
|00005060| 3d 28 28 37 5e 31 29 2b | 31 32 29 25 31 30 3d 31 |=((7^1)+|12)%10=1|
|00005070| 38 25 31 30 3d 38 0d 53 | 4e 53 74 72 5b 36 5d 3d |8%10=8.S|NStr[6]=|
|00005080| 6d 79 56 61 6c 54 6f 43 | 68 61 72 28 38 5e 31 29 |myValToC|har(8^1)|
|00005090| 3d 27 39 27 0d 0d 41 66 | 74 65 72 20 53 74 65 70 |='9'..Af|ter Step|
|000050a0| 20 43 20 28 69 3d 34 2c | 6b 3d 33 29 0d 73 70 65 | C (i=4,|k=3).spe|
|000050b0| 63 69 61 6c 42 3d 28 28 | 28 27 35 27 2d 27 30 27 |cialB=((|('5'-'0'|
|000050c0| 29 5e 31 29 2b 33 2b 38 | 2b 36 29 25 31 30 3d 28 |)^1)+3+8|+6)%10=(|
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|00005150| 30 0d 53 4e 53 74 72 5b | 31 30 5d 3d 6d 79 56 61 |0.SNStr[|10]=myVa|
|00005160| 6c 54 6f 43 68 61 72 28 | 30 5e 31 29 3d 27 31 27 |lToChar(|0^1)='1'|
|00005170| 0d 0d 41 66 74 65 72 20 | 53 74 65 70 20 43 20 28 |..After |Step C (|
|00005180| 69 3d 36 2c 6b 3d 31 29 | 0d 73 70 65 63 69 61 6c |i=6,k=1)|.special|
|00005190| 42 3d 28 28 28 27 31 27 | 2d 27 30 27 29 5e 31 29 |B=((('1'|-'0')^1)|
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|000051d0| 43 68 61 72 28 35 5e 31 | 29 3d 27 34 27 0d 0d 74 |Char(5^1|)='4'..t|
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|00005240| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
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|00005260| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00005270| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
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+--------+-------------------------+-------------------------+--------+--------+
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