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## Tricky Substitution Equation

 Category: Trick Submitted By: eighsse Fun: (2.35) Difficulty: (2.73)

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."

What is the correct answer?

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Comments on this teaser

 Posted by charlottes-odd 12/17/13 Another good one eighsse! :) Posted by eighsse 12/17/13 Thanks charlotte :) Posted by koin_era345 12/20/13 I don't know if this should be in trick, but I like it nonetheless. Posted by eighsse 12/20/13 It's in Trick because at first sight, the X's will likely be considered letters, which must stand for digits. But they really are multiplication signs, not letters. The only other category I might consider it to be is Situation, as it's somewhat unfair to the solver, considering that the body of the teaser is typed with an actual letter "X" character. So it's written with a third-person perspective since an "X" and a multiplication sign, in writing, are generally interchangeable. This might make it more fit for Situation, but I still feel it is more of a Trick. Posted by dalfamnest 07/04/14 As a trick, I think it's great - top marks!! Thanks for something new and different. :D :D Posted by eighsse 07/04/14 Thanks dalfamnest, glad you enjoyed it :) Posted by Zag24 07/21/14 Nicely done. Of course, I can beat your solution with my own. No one said that the digits were DECIMAL digits. (Back in the old days, I used to have to add and subtract hexidecimal values all the time. But there's no reason these digits aren't in base 10000000.) Posted by eighsse 07/21/14 Hah! This is true. Very nice, zag. Posted by sarggames 11/04/14 AGAIN I DID IT Posted by flower-girl 03/14/15 Too hard & boring. Posted by Captain_Obvious 03/28/15 It's a good teaser but I don't really understand why Karl said Larry's answer was incorrect when the answer was 4 Posted by eighsse 03/28/15 Because he asked what the LARGEST possible value is, not just any valid value. Posted by Eminem 06/20/15 Solved it its 8 Posted by Eminem 06/20/15 Solved it its 8 Posted by Eminem 06/20/15 Solved it its 8 Posted by eighsse 07/01/15 Good job, Eminem! Good job, Eminem! Good job, Eminem! Posted by TheRiddleTroll 12/10/16 The X's don't have to be multiplication signs to get 8. In algebra, putting variable next to each other assumes that you're multiplying them. This really was just a math question, not a trick. Posted by TheRiddleTroll 12/10/16 The X's don't have to be multiplication signs to get 8. In algebra, putting variable next to each other assumes that you're multiplying them. This really was just a math question, not a trick. Posted by eighsse 12/11/16 RiddleTroll, that's very true. I somehow didn't think about that, but I guess the one thing that indicates that these are not algebraic variables is the title. A substitution equation is a particular type of puzzle like this, in which letters are not typical variables, but just placeholders. However, you're still right, because the quotation in the puzzle does not specify that. My mistake!

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