There are several red and several white boxes on the table, each of these boxes contains at least one ball. A positive integer number not exceeding 1111 is written on each of these balls.
- Any two boxes contain different number of balls.
- No box contains two balls with the same number.
- For each 1 ≤ i ≤ 1111 there is at most one red box containing ball number i.
- For each 1 ≤ i ≤ 1111 there is at most one white box containing ball number i.
- For any two balls with numbers i and j, where 1 ≤ i ≤ 1111, 1 ≤ j ≤ 1111 and i ≠ j there is at most one box containing these two balls.
Find the maximal possible number of boxes on the table.
Correct Solutions by,
- Toshihiro Shimizu Kawasaki, Japan
- Roger Bengtsson Lund, Sweden
- Magnus Jakobsson Lund, Sweden
- Arda Karahan Trabzon Fen Lisesi
- Arda Choi Min Kyu South Korea
- Burak Bulak Bilkent University
- Serkan Yaşar
Solution: 2401a.pdf (bilkent.edu.tr)