Suggestion

  1. In the four-by-four version of the game, starting with pattern

    4 by 4 pattern where counting left to right along each row from top to bottom, the second, fourth, sixth, eighth, tenth, twelfth, fourteenth and sixteenth tiles are black.

    explain why it is impossible to reach a pattern with only one white counter.

When a row or a column is flipped, what happens to the number of whites in that row or column?

  1. In the five-by-five game, explain why any sequence of moves which begins

    5 by 5 pattern where counting the same way as in the previous pattern, all odd-numbered tiles are black.

    and ends with an all-white pattern, must involve an odd number of moves. What is the least number of moves needed? Give reasons for your answer.

Again, when a row or a column is flipped, what happens to the number of whites in that row or column?

Can we see how to get to an all-white board? Can we show that it can’t be done in fewer moves?