Comments on: SET Tic-Tac-Toe
https://blog.tanyakhovanova.com/2020/06/set-tic-tac-toe/
Mathematics, applications of mathematics to life in general, and my life as a mathematician.Fri, 26 Jun 2020 17:51:44 +0000
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By: CristÃ³bal Camarero
https://blog.tanyakhovanova.com/2020/06/set-tic-tac-toe/#comment-13125
Fri, 26 Jun 2020 17:51:44 +0000https://blog.tanyakhovanova.com/?p=1463#comment-13125SET tic-tac-toe is tic-tac-toe over a torus. We can see that 5 points/cards are enough to get a whole line by a counting argument. As 2 points define a line, if we were to get 5 points with only 2 points per line we would get at least 10 lines. There are 12 lines, but some are parallel, having 4 different directions. There are 3 lines in each direction. We could try to divide the expected 10 lines as 10=3+3+2+2 or 10=3+3+3+1, this is, a partition of the 10 lines with each summand representing the number of lines with 2 selected points for each of the four directions. However, if we have 2 points in all the lines of a given direction then we have at least 6 points.
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