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| Take five! (Posted on 2006-09-21) |
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I selected five different integer numbers between 1 and 7 (both inclusive) but if I told you their product, you wouldn't be able to deduce whether their sum was odd or even. What is their product?
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Submitted by Federico Kereki
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Rating: 4.0000 (2 votes)
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Solution:
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420. Giving the product of the five chosen numbers is equivalent to giving the product of the two remaining numbers. Of these products, the only ones that can be achieved in more than one way are are 6 (1x6 and 2x3) and 12 (3x4 or 2x6). However, in the former case, the sum of the other five numbers is always odd, so the latter case must be the correct one, and my original product is 7!/12, or 420. |
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