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?
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Maybe start with the 2 by 2 array and work your way out? – hardmath Mar 01 '14 at 12:33
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There is an easy answer to this question, but giving it would take away the pleasure of thinking it through. What have you tried? – Mark Bennet Mar 01 '14 at 12:33
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I changed the tag from calculus to recreational mathematics. – Mark Bennet Mar 01 '14 at 12:35
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1I would try a $3 \times 3$ grid for a start. – Mark Bennet Mar 01 '14 at 12:35
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There are 6 starting positions, did you try each solution by hand ? – Sylvain Biehler Mar 05 '14 at 14:03
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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?
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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.
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