S is the set \(\left\{1,\;2,\;3,\;\dots,\;1000000\right\}\). 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 \(\left\{a+x_i\vert a\in A\right\}\) are all pairwise disjoint.
| Attributes | Олімпіадна |
|---|---|
| Source | International Mathematical Olympiad |
| Year | 2003 |
| Number | 1 |
| Difficulty | 10.0 |
| Themes |