SOLUTION: 25 coins are arranged in a 5 array. A fly lands on 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

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Question 749275: 25 coins are arranged in a 5 array. A fly lands on 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?

1- Is there a pattern in good and bad starting points?
2- what if some of the arrays have coins missing?
3- what if diagonal moves are permitted? Other moves?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
There are lots of ways but the easy one is the "spiral" or "snail" method.

1- Is there a pattern in good and bad starting points?
You can start anywhere.

2- what if some of the arrays have coins missing?
It depends on which ones are missing.  Suppose we
take out, say, the last 7 circles the fly hoped on.



The fly can hop onto all those. But if we take out a whole row, 
like this:



There is no way possible to get across that missing row.

3- what if diagonal moves are permitted? Other moves?
We don't need diagonal moves or any other kind of moves.  It's easy
enough as it is.

Edwin