Question 100
Simon plays a game on an $n \times n$ grid of cells. Initially, each cell is filled with an integer. Every minute, Simon picks a cell satisfying the following:
(a) The magnitude of the integer in the chosen cell is less than $n^n$
(b) The sum of all the integers in the neighboring cells (sharing one side with the chosen cell) is non-zero
Simon then adds each integer in a neighboring cell to the chosen cell.
Show that Simon will eventually not be able to make any valid moves.
(a) The magnitude of the integer in the chosen cell is less than $n^n$
(b) The sum of all the integers in the neighboring cells (sharing one side with the chosen cell) is non-zero
Simon then adds each integer in a neighboring cell to the chosen cell.
Show that Simon will eventually not be able to make any valid moves.