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MMO 372 Moscow MO 1957 divide a_i <= a_{i+1} <= 2a_i, into 2 groups

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March 20, 2021
combinatoricsSumnumber theory

Problem Statement

Given nn integers a1=1,a2,...,ana_1 = 1, a_2,..., a_n such that ai≤ai+1≤2aia_i \le a_{i+1} \le 2a_i (i=1,2,3,...,n−1i = 1, 2, 3,..., n - 1) and whose sum is even. Find whether it is possible to divide them into two groups so that the sum of numbers in one group is equal to the sum of numbers in the other group.
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