# 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.)

### This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

 What if applet does not run?

Explanation

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.

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