How do I repair the boat?

Hint 1 of 16:

First, you need to open the gate.

Hint 2 of 16:

Once the gate is open, you need to get rid of the water in the boat.

Hint 3 of 16:

A bucket would be useful.

Hint 4 of 16:

Unfortunately, you don't have a bucket.

Hint 5 of 16:

What about some other kind of container?

Hint 6 of 16:

Like a shoe, for instance.

Hint 7 of 16:

A wooden shoe, to be more specific.

Hint 8 of 16:

Use the wooden shoe on the water.

Hint 9 of 16:

Now you need to plug the leak.

Hint 10 of 16:

You'll need to get the cork back. (See "I can't find my cork" for details/)

Hint 11 of 16:

The cork alone won't plug the hole.  It's too small.