Tricky Substitution Equation
Trick brain teasers appear difficult at first, but they have a trick that makes them really easy.
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?
HintThe 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 "ZY=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.
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Answer
The answer is 8. Karl never said that the letters X, Y, and Z are used. Only the letters Y and Z are used in the equation, while the X's are actually multiplication signs. So the teaser actually reads: "Y times Z, minus Y times Y, equals Y," or YZ  Y^2 = Y
Y (ZY) = Y
ZY = 1
Z = Y+1
So, any digits can be used, as long as they are different and Z is one greater than Y. Z can be 9, with Y being 8, giving "9*8  8*8 = 8." This is true, so the answer is valid.
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Comments
charlottesodd
Dec 17, 2013
 Another good one eighsse! 
eighsse
Dec 17, 2013
 Thanks charlotte 
koin_era345
Dec 20, 2013
 I don't know if this should be in trick, but I like it nonetheless. 
eighsse
Dec 20, 2013
 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 thirdperson 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. 
dalfamnest
Jul 04, 2014
 As a trick, I think it's great  top marks!! Thanks for something new and different. 
eighsse
Jul 04, 2014
 Thanks dalfamnest, glad you enjoyed it 
Zag24
Jul 21, 2014
 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.) 
eighsse
Jul 21, 2014
 Hah! This is true. Very nice, zag. 
sarggames
Nov 04, 2014
 AGAIN I DID IT 
flowergirl
Mar 14, 2015
 Too hard & boring. 
Captain_Obvious
Mar 28, 2015
 It's a good teaser but I don't really understand why Karl said Larry's answer was incorrect when the answer was 4 
eighsse
Mar 28, 2015
 Because he asked what the LARGEST possible value is, not just any valid value. 
Eminem
Jun 20, 2015
 Solved it its 8 
Eminem
Jun 20, 2015
 Solved it its 8 
Eminem
Jun 20, 2015
 Solved it its 8 
eighsse
Jul 01, 2015
 Good job, Eminem!
Good job, Eminem!
Good job, Eminem! 
TheRiddleTroll
Dec 10, 2016
 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. 
TheRiddleTroll
Dec 10, 2016
 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. 
eighsse
Dec 11, 2016
 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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