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Take five! (Posted on 2006-09-21) Difficulty: 2 of 5
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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Solution 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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