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]]

Revision as of 10:04, 24 November 2019

$S$ is the set $\{1, 2, 3, \dots ,1000000\}$. 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 $\{a + x_i \mid a \in A\}$ are all pairwise disjoint.


See Also

2003 IMO (Problems) • Resources
Preceded by
'
1 2 3 4 5 6 Followed by
Problem 2
All IMO Problems and Solutions
Invalid username
Login to AoPS