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.
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.