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