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Problem of the Month – January 2024

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)