For the sum, difference and product to be odd, odd and even, respectively, the smaller number must be odd and the larger one even (if the smaller one were even, so would be the larger).
The smallest larger number with each of the four smallest odd numbers is (with the eight numbers in the left two columns and their sum on the right):
1 2 3
3 6 9
5 10 15
7 14 21
---
48 is the total of all 8 numbers.
For task II, with sum, difference and product all even, both numbers must be even:
The smallest non-overlapping groups are:
2 4 6
6 12 18
8 16 24
10 20 30
---
78
For part III, both numbers must be odd:
The smallest groups are:
1 3 4
5 15 20
7 21 28
9 27 36
---
88
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Posted by Charlie
on 2012-03-03 15:12:55 |
solutions
