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PrintFINAL ROUND
Belarus counting and probability
Problem
Is it possible to partition a set of positive integers into some disjoint subsets so that in each subset one of the numbers is equal to the sum of all other numbers of this subset if
Solution
a) Yes, it is possible; the desired partition exists. For example, see the following table:
In each subset, one of the numbers is equal to the sum of the others.
| 20 | 19 | 18 | 17 | 16 | 15 |
|---|---|---|---|---|---|
| 14 | 12 | 10 | 13 | 11 | 9 |
| 6 | 7 | 8 | 4 | 5 | 1, 2, 3 |
Techniques
Other