How in the world do you solve this?

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mathwoman

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Each letter in each question stands for a 1-digit number. No two letters may stand for the same number. Find a value for each letter.

DYE × IS = SIGHT

(Use the numbers: 9, 3, 7, 2, 1, 4, 5, and 8)
 
One way to solve this is brute force, making educated guesses. In other words, start trying experiments.

(I'm assuming that you know how to multiply a 3-digit number by a 2-digit number by hand.)

Since the last digit of SIGHT comes from the first multiplication (which is S times E), we know that the last digit in the product S*E is T.

If S = 2 and E = 4, for example, then we know T = 8.

If S = 3 and E = 9, for example, then we know T = 7.

You could also form a few 3- and 2-digit numbers from the given digits, to exeriment on how big the numbers DYE and IS need to be in order to obtain a 5-digit product. I'm thnking that, if D is small, then I must be big, and vice versa, but I didn't experiment.

Since the first digit of SIGHT comes from the first digit in the product of I times D, we know that the first digit of I*D must be S.

These three facts are a start. Now take cases, based on these facts, and plug-and-chug. Through a process of elimination, you'll arrive at the solution, after sufficient effort (assuming a solution exists).
 
I think this is the answer

DYE = 579
IS = 42
SIGHT = 24318

579 * 42 = 24318

And I solved it with brute force, exhausting all permutations of D Y E I S G H T as 9, 3, 7, 2, 1, 4, 5, 8
 
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