Question 403660: Jill discovered an interesting multiplication problem. She wrote it in code by replacing each digit with a different letter. Identical letters represent identical digits. Can you crack the code? STRAW X 4 = WARTS.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Right away, we can conclude that S = 2, since STRAW < 25000, and S must be a nonzero multiple of 2. Since S = 2, it follows that W = 8 or 9, but since 9 x 4 ≡ 6 (mod 10) and 8 x 4 ≡ 2 (mod 10) we obtain W = 8.
Since STRAW <= 89999, then T = 0, 1, or 2.However T2 must be a multiple of 4 so T = 1. Now, we have
21RA8 * 4 = 8AR12
If we multiply 21RA8 by 4 using the standard multiplication method, we get the tens digit, 1, is congruent to 4A + 3 (modulo 10). Therefore, 4A ≡ 8 modulo 10, A = 2 or 7. Since no two digits are identical, A = 7. Now, we have
21R78 * 4 = 87R12
Here I pretty much guessed and checked, obtaining R = 9. Therefore,
21978 * 4 = 87912 which is a true equation.
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