This is an entry into the 29th fortnightly topic challenge - Retrograde Analysis.
Alice and Bob were playing a game of Sudoku-Janpu.
Alice: I win.
Bob: (looking at the board) Oh man, not again!
Alice: You could have won before; I made a mistake.
Alice: (pointing at the board several times) See, if you went there instead of there I'd have had no legal move ... I should have gone there instead of there.
Bob: Aw... that makes it even worse! Want another game? This time I'm going to win.
Alice: (chuckles) We'll see about that!
This was the final position:
For you to work out:
How did Alice win? How could Bob have won?
Both answers require proof.
Sudoku-Janpu is a 2-player game played on a blank sudoku grid. Janpu means jump in Japanese.
- The first player can play anywhere
- After that, players have to play exactly a knight's jump away from the last play
- A play consists of writing a number in a blank square, as long as the number is not in the same row, column or 3x3 box
- The first person who cannot make a valid play loses