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Sets with Properties

Source: 2012 IrMO Paper 1 Problem 1

February 16, 2018
combinatorics

Problem Statement

Let C={1,22,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}C=\{1,22,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20\} and let S={4,5,9,14,23,37}S=\{4,5,9,14,23,37\} Find two sets AA and BB with the properties (a) A∩B=∅A\cap B=\emptyset. (b) A∪B=CA\cup B=C. (c) The sum of two distinct elements of AA is not in SS. (d) The sum of two distinct elements of BB is not in SS.
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