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## Tricky Substitution Equation

 Category: Trick Submitted By: eighsse Fun: (2.37) Difficulty: (2.75)

Karl and his friend Larry are always pulling trick brain teasers on each other. Larry has been getting the best of Karl all too often lately, so Karl really wants to get him back. He comes up with a good one, and writes the following on a piece of paper:
" YXZ
- YXY
= Y"
He shows it to Larry, and says, "Each different letter in this equation stands for a different digit. All instances of a given letter stand for the same digit. There are multiple true solutions, but what is the greatest digit that Y can stand for in a true solution?" Larry scans the equation over and over. He can't come up with any way that the answer could not be 4. "The answer must be four," he says, with confidence. Karl smiles and replies, "Sorry, you're incorrect."

### Hint:

The answer is not "Karl is lying. The answer really is 4."

And for anyone wondering, the reason 4 is the expected answer is as follows:
The first two digits, "YX," in the first two lines are identical, canceling out to 0, no matter what they stand for. Then the equation resolves to "Z-Y=Y," in which case Z must be 2*Y. This limits Y to a maximum of 4 because Z is a single digit and cannot be greater than 9.