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 Take five! (Posted on 2006-09-21)
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?

 See The Solution Submitted by Federico Kereki Rating: 4.0000 (2 votes)

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 computer assisted solution | Comment 1 of 4

Here are the products and sums, identified by the two integers not included, and sorted by product:

`nos. not used  prod   sum     6     7   120    15     5     7   144    16     5     6   168    17     4     7   180    17     4     6   210    18     3     7   240    18     4     5   252    19     3     6   280    19     3     5   336    20     2     7   360    19     3     4   420    21     2     6   420    20     2     5   504    21     2     4   630    22     1     7   720    20     1     6   840    21     2     3   840    23     1     5  1008    22     1     4  1260    23     1     3  1680    24     1     2  2520    25`

The product 420 is the only one that could correspond with either an even or an odd sum. It is obtained by leaving out either 3 and 4 (odd total) or 2 and 6 (even total).

 Posted by Charlie on 2006-09-21 13:54:59

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