Problem
of the
Week
PROBLEM 135

Many thanks to Sudipta Das (Calcutta, India) for suggesting the following problem.

Randomly rearrange the numbers 1,2,3,...9, and write the new arrangement below the original one. Subtract the two and multiply together the resulting differences. See the example below.

I bet that I can guess whether your product is odd or even. Should you accept my bet?
Please explain your reasoning fully.

You now make me the same bet with the numbers 1,2,3,...,10. Should I accept your bet?

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ã2002 Alberto L. Delgado