Correction:

One thing I forgot to mention in the "Differences" game is: No integer may receive more than one mark on the same side. Otherwise, the game might not end. A "\" and an "X" are equivalent marks, but the "\" simply indicates a player's most recent move.

Basically, the distance you want to travel from your most recent position must not have a mark next to it on your opponent's side, and you can never visit any integer more than once.

Obviously, the spacing is wrong in that sample game. So I'll just describe the moves in each turn. The game is played on the integers , listed vertically.

Turn-1: Player-1 marks a "\" to the left of 4.

Turn-2: Player-2 marks a "\" to the right of 4.

Turn-3: Player-1 marks an "X" to the left of 4, and marks a "\" to the left of 2. This is ok because |4-2|=2 has not been marked on the right.

Turn-4: Player-2 marks an "X" to the right of 4, and marks a "\" to the right of 1. This is ok because |4-1|=3 has not been marked on the left.

Turn-5: Player-1 marks an "X" to the left of 2, and marks a "\" to the left of 5. This is ok because |5-2|=3 has not been marked on the right.

Turn-6: Player-2 marks an "X" to the right of 1, and marks a "\" to the right of 2. This is ok because |2-1|=1 has not been marked on the left.

Turn-7: Player-1 cannot move, so Player-2 moves again. Player-2 marks an "X" to the right of 2, and marks a "\" to the right of 5. This is ok because |5-2|=3 has not been marked on the left.

The game is now over, because neither player can mark any "open" number on his side ("open" meaning that the number has not been marked on his side).