S L I D E

- D E A N

---------

3 6 5 1

Each of seven digits from 0-9 are represented by a different letter above such that the subtraction is true.

What word represents 3651?

Answer

3651 represents LENS.

Let's assign possible values to each letter and then use trial-n-error.

S must be 1.

Then D (under L) must be greater than 5. If D is 6, then L is 0. But then A must be 0 or 1 which is impossible. Hence, the possible values of D are 7, 8 or 9.

N must be E + 1. Also, D must be A + 5 as the possible values of D are 7, 8 or 9, D can not be (10+A) + 5.

Now using trial-n-error, we get S=1, I=2, L=3, A=4, N=5, E=6 and D=9

S L I D E 1 3 2 9 6

- D E A N - 9 6 4 5

-------------- --------------

3 6 5 1 L E N S

Hence, 3651 represents LENS.

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