YE * ME = TTT find Y,E,M,T and Y+M+E+T

If YE and ME
each end in then TTT
ends in     1 1 ←  No good (T ≠ E). 2 4 ←  444 = 4 · 111 = 4 · 3 · 37. But 37 is prime.
And 12 x 37 does not work (2 ≠ 7). 3 9 ←  999 = 9 · 3 · 37 = 27 · 37 = 999. But 7 ≠ 3. 4 6 ←  666 = 6 · 3 · 37 = 18 · 37 = 666, no good. 5 5 ←  555 = 5 · 3 · 37 = 15 · 37 = 555, no good. 6 6 ←  No good, see above. 7 9 ←  This works! We have 2 7  ·  3 7  =  9 9 9 Y E  ·  M E  =  T T T   And 2 + 7 + 3 + 9 = 21. 8 4 ←  No good, see above. 9 1 ←  111 = 3 · 37, impossible. 0 0 ←  No good (T ≠ E).
So 27 · 37 is the only product that works, and the answer is 21.
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