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### Tetromino tilings of a 4x5 rectangle with minimal diversity

I suspect the answer is with a possible tiling of First of all, I found that achieving the score of exactly 2 wasn't very hard with N = 4, so I focused on maximizing the ratio of the 5x I board (...
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Here's a simple way to guarantee a win with Partition $\{1,\dots,11\}$ into $A=\{1,\dots,6\}$ and $B=\{7,\dots,11\}$. By the pigeonhole principle, every draw of $5$ numbers must contain at least \$\...