Date Game

This two players game starts with a date in January. Players take turns increasing either the month or the number, but not both. At any time, the applet is required to show a valid date. The player to reach December 31 wins the game. (To modify the date click repeatedly on either the month or the date and then press Move.)

Explanation

Copyright © 1996-2009 Alexander Bogomolny

Without any doubt the Date game is impartial. As such, every possible position in the game is equivalent to a Nim-heap. Starting with the goal of December 31 which has the Grundy number of 0, we expand the table leftward and upward a square at a time using the Mex Rule. The result is below:

The P-positions lie on the diagonal emanting from the lower right corner. This is where you'd like to be after your move.

The game is very much a Nim with two heaps. The fact that some months are shorter than others has very little effect on the location of P-positions.

Copyright © 1996-2009 Alexander Bogomolny