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

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− | <math>S</math> is the set <math>\ | + | <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. |

## Revision as of 09:39, 24 November 2019

is the set . Show that for any subset of with elements we can find distinct elements of , such that the sets are all pairwise disjoint.