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?
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).
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Posted by Charlie
on 2006-09-21 13:54:59 |
computer assisted solution
