Difference between revisions of "2003 IMO Problems/Problem 1"
m (Problems in tex formulas) |
m (Added see also box and a category) |
||
| Line 1: | Line 1: | ||
<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. | ||
| + | |||
| + | |||
| + | ==See Also== | ||
| + | {{IMO box|year=2003|before=|num-a=2}} | ||
| + | [[Category:Olympiad Combinatorics Problems]] | ||
is the set 
. Show that for any subset 
of 
elements we can find 
distinct elements 
of 
are all pairwise disjoint.
