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Problem of the Month – April 2026

Alice and Bob play a game on a grid consisting of 2026 rowsande 9 columns. At the beginning of the game Alice inserts a number to each unit square such that all numbers of each row are different. After that they take turns to make move starting with Bob. Bob in each move chooses a number not chosen before and colour all unit squares containing this number to red. Alice in each move chooses a number not chosen before and colour all unit squares containing this number to blue. Suppose that Alice can guarantee that after colouring all unit squares there are at least N rows containing only blue unit squares. Determine the maximal possible value of N.

 

Correct Solutions by,

  • Toshihiro ShimizuKawasaki, Japan
  • Hannes NilssonCopenhagen, Denmark
  • Güneş ParlakgülUniversity of California, Berkeley, USA
  • Mustafa KaynakGaziantep
  • Özgür SoysalStanford University, USA
  • Magnus JakobssonLund, Sweden
  • Roger BengtssonLund, Sweden
  • Murat BurçSoma, Manisa
  • Mehmet SarakBilkent University
  • Muhammed CengizBilkent University

Solution: https://math.bilkent.edu.tr/Problem/2604a.pdf