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Fit as many of the tetromino tiles (on the right) as possible into the 9 × 9 9\times 9 grid, with both rotation and reflection allowed.

Then give your answer as the least possible number of empty cells in the 9 × 9 9\times 9 grid unoccupied by these tiles.


The answer is 17.

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2 solutions

Bj Fread
Oct 22, 2017

Simple Tetris: you put them in horizontal rows 3 times, each row will have 1 empty cell, or 6 total. Then in the top row, the pieces go up and down, leaving 2 empty cells per piece, (8) and there will be 3 empty cells at the end of the row. Or stick with the horizontal rows and leave the entire top 9 cells empty. Either way, 17 total.

That's not a general proof...

Marina Longnickel - 3 years, 7 months ago
Luis Salazar
Oct 24, 2017

I just tried manually, ended with this.

I'd love to see a proof.

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