Substitute digits for the letters to make the following Division true
O U T

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S T E M | D E M I S E

| D M O C

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T U I S

S T E M

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Z Z Z E

Z U M M

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I S T
Note that the leftmost letter can't be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter M, no other letter can be 3 and all other M in the puzzle must be


Answer:

C=0, U=1, S=2, T=3, O=4, M=5, I=6, Z=7, E=8, D=9

It is obvious that U=1 (as U*STEM=STEM) and C=0 (as I-C=I).

S*O is a single digit and also S*T is a single digit. Hence, their values (O, S, T) must be 2, 3 or 4 (as they can not be 0 or 1 or greater than 4).

Consider, STEM*O=DMOC, where C=0. It means that M must be 5. Now, its simple. O=4, S=2, T=3, E=8, Z=7, I=6 and D=9.
O U T 4 1 3

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S T E M | D E M I S E 2 3 8 5 | 9 8 5 6 2 8

| D M O C | 9 5 4 0

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T U I S 3 1 6 2

S T E M 2 3 8 5

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Z Z Z E 7 7 7 8

Z U M M 7 1 5 5

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I S T 6 2 3