MathDB

5

Part of 1998 Poland - Second Round

Problems(1)

Poland 1998

Source:

10/16/2011
Let a1,a2,…,a7,b1,b2,…,b7≥0a_1,a_2,\ldots,a_7, b_1,b_2,\ldots,b_7\geq 0 be real numbers satisfying ai+bi≤2a_i+b_i\le 2 for all i=1,7‾i=\overline{1,7}. Prove that there exist k≠mk\ne m such that ∣ak−am∣+∣bk−bm∣≤1|a_k-a_m|+|b_k-b_m|\le 1.
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