MathDB
TOT 1999 Autumn AS5 1, 2 , ... , n divided into 2 groups

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May 11, 2020
partitionSumcombinatoricsSubset

Problem Statement

(a) The numbers 1,2,...,1001, 2,... , 100 are divided into two groups so that the sum of all numbers in one group is equal to that in the other. Prove that one can remove two numbers from each group so that the sums of all numbers in each group are still the same. (b) The numbers 1,2,...,n1, 2 , ... , n are divided into two groups so that the sum of all numbers in one group is equal to that in the other . Is it true that for every suchn>4 n > 4 one can remove two numbers from each group so that the sums of all numbers in each group are still the same?
(A Shapovalov) [(a) for Juniors, (a)+(b) for Seniors]
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