On the Subject of Coinage

Spoiler warning for "The Impossible Chessboard Puzzle".

There are 64 coins, in an 8×8 grid, each either heads or tails.

  • Take the serial number, and replace each character with a 1 if it's within 5-9 or N-Z, and 0 otherwise. Call this the hamming code.
  • Next, create another 6-digit code. Start by counting the number of heads in the highlighted (black) region in the 1st table. If the sum is even, the 1st digit is 0, otherwise 1. Repeat the above for the other 5 tables to obtain 5 more digits, which gives you another 6-digit code.
  • To solve the module, press the coin in which — when flipped - will make both 6-digit codes the same. Flipping an incorrect coin gives a strike.
1st
8
7
6
5
4
3
2
1
a b c d e f g h
2nd
8
7
6
5
4
3
2
1
a b c d e f g h
3rd
8
7
6
5
4
3
2
1
a b c d e f g h
4th
8
7
6
5
4
3
2
1
a b c d e f g h
5th
8
7
6
5
4
3
2
1
a b c d e f g h
6th
8
7
6
5
4
3
2
1
a b c d e f g h