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2024 InIMC keystage3-IWYMIC individual Question 12

xIMC · 2024 InIMC keystage3-IWYMIC individual

Question 12

Each square of an infinite grid has been filled with exactly one digit. Elsa places an O-tetromino on this grid covering four squares along the grid lines:

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The minimum number of different digits used to fill the infinite grid so that the four squares will have different digits, regardless the position of the O-tetromino, is 4. The following grid is an example of such filling.

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When Elsa places a L-tetromino on this grid covering four squares along the grid lines, what is the minimum number of different digits that must be used for the infinite grid so that the four squares covered by the L-tetromino will always have different digits? (Elsa may flip or rotate the L-tetromino)

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