# Difference between revisions of "2003 IMO Problems/Problem 1"

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<math>S</math> is the set <math>\{1, 2, 3, \dots ,1000000\}</math>. Show that for any subset <math>A</math> of <math>S</math> with <math>101</math> elements we can find <math>100</math> distinct elements <math>x_i</math> of <math>S</math>, such that the sets <math>\{a + x_i \mid a \in A\}</math> are all pairwise disjoint. | <math>S</math> is the set <math>\{1, 2, 3, \dots ,1000000\}</math>. Show that for any subset <math>A</math> of <math>S</math> with <math>101</math> elements we can find <math>100</math> distinct elements <math>x_i</math> of <math>S</math>, such that the sets <math>\{a + x_i \mid a \in A\}</math> are all pairwise disjoint. | ||

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+ | ==See Also== | ||

+ | {{IMO box|year=2003|before=|num-a=2}} | ||

+ | [[Category:Olympiad Combinatorics Problems]] |