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, 2024

Number theory Difficulty 5.0 AIME, harder Prove it United Kingdom

The numbers 1, 2, 3, 4 and 5 are used once each in some order substituting for the letters in the series of powers $M^{A^{T^{H^S}}}$ . In how many of the arrangements is the units digit of the value of this expression equal to 1?

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