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IMO LongList 1967, Mongolia 1

Source: IMO LongList 1967, Mongolia 1

December 16, 2004
combinatoricscountingIMO ShortlistIMO Longlist

Problem Statement

Given m+nm+n numbers: ai,a_i, i=1,2,…,m,i = 1,2, \ldots, m, bjb_j, j=1,2,…,n,j = 1,2, \ldots, n, determine the number of pairs (ai,bj)(a_i,b_j) for which ∣i−j∣≥k,|i-j| \geq k, where kk is a non-negative integer.
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