Product = TTT

In the following equation, each of the letters represents a uniquely different digit in base ten. Suppose:

(YE)(ME) = TTT, where the number YE is less than ME in the product on the left.

Then the sum E + M + T + Y equals:

  1. 19
  2. 20
  3. 21
  4. 22
  5. 24


Show/Hide Solution

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 (c).

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