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Prove or disprove the statement that it is possible to tile a $10\times10$ grid with 10 T-shaped tetrominoes and 15 S-shaped tetrominoes. (It is allowed to rotate or flip any piece as desired.)

I have tried multiple colorings, including the chessboard and alternating row patterns. However I still can't find a coloring pattern that solves the problem.

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1 Answer 1

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6
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 1  1  1 15 16  2  2  2  3  3 
12  1 15 15 16 16  2  3  3 23 
12 12 15  4  4 16 18 22 23 23 
13 12  4  4 17 18 18 22 22 23 
13 13  5  5 17 17 18 20 22 24 
13  6  6  5  5 17 20 20 24 24 
 6  6  7  7  8  8 19 20 25 24 
14  7  7  8  8 19 19 21 25 25 
14 14  9 10 10 19 21 21 11 25 
14  9  9  9 10 10 21 11 11 11
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