25 coins are arranged in a 5 by 5 array.

Question

25 coins are arranged in a 5 by 5 array. A fly lands on one and tries to hop on to every coin exactly once, at each stage moving only to an adjacent coin in the same row or column. Is this possible?

Answer 1

Try coloring the array like a checkerboard.

How many white and black squares there are? What's the difference between starting on a white vs black square?

Answers:

Since the number of all squares is 25 which is an odd number, the color of the square you start on must be the same as the color you end on, because the colors always alternate. But one color is more prevalent than the other, so if you start on the one with less squares, you can't possibly visit all squares.