Difference between revisions of "2003 IMO Problems/Problem 1"
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| − | <math>S</math> is the set <math>\set{1, 2, 3, | + | <math>S</math> is the set <math>\set{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>\set{a + x_i \mid a \in A}</math> are all pairwise disjoint. |
| − | \mid a \in A}</math> are all pairwise disjoint. | ||
Revision as of 09:36, 24 November 2019
is the set $\set{1, 2, 3, \dots ,1000000}$ (Error compiling LaTeX. Unknown error_msg). Show that for any subset 
of with 
elements we can find 
distinct elements 
of , such that the sets $\set{a + x_i \mid a \in A}$ (Error compiling LaTeX. Unknown error_msg) are all pairwise disjoint.
