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

(Typed in the problem from official pdf)
 
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<math>S</math> is the set <math>\set{1, 2, 3, . . . , 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
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<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

$S$ is the set $\set{1, 2, 3, \dots ,1000000}$ (Error compiling LaTeX. ! Undefined control sequence.). Show that for any subset $A$ of $S$ with $101$ elements we can find $100$ distinct elements $x_i$ of $S$, such that the sets $\set{a + x_i \mid a \in A}$ (Error compiling LaTeX. ! Undefined control sequence.) are all pairwise disjoint.

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