Problem of the Summer: 2014-08-25

Due the First Week of Classes, or Whenever ...

The Suicidal King

This problem did not get a definitive answer.  The only answer submitted was "I think he can".  We who posed this problem don't know the answer, either.  So this puzzle is open to anyone - including undergraduates, graduate students, professors, and pre-schoolers.   

Imagine a 1000 x 1000 chessboard on which a white king and 499 black rooks are placed at random.  Suppose the king goes bonkers and wants to kill himself.  Can he always reach a threatened square in a finite number of moves if Black is trying actively to avoid this?

All answers should be clearly explained.  Mathematics is about logic and reasoning, not just about getting a number and putting a box around it.

Submit your answers to this special puzzle to Stephen.Wilson or

Winning solutions and a summary of scores will be posted on the POTW bulletin board. This bulletin board is located near the bottom of the big stairway joining the first and second floor of the Adel Math Building.