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I have a collection of eleven flashcards. Out of all the flashcards like them that you could make, only these eleven are special. Here, I'll show them to you:

enter image description here

Hey! Somebody's slipped a fake card into my collection!
Which of these twelve cards is not special, and how are the other eleven special?

Text version of image:

  39    49    59    29  
+ 18  + 49  + 19  + 57  
= 57  = 98  = 77  = 86

  29    18    19    69  
+ 38  + 28  + 79  + 29  
= 67  = 46  = 98  = 98  

  16    18    39    37  
+ 19  + 17  + 59  + 19  
= 35  = 35  = 98  = 56
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2 Answers 2

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The odd one out I believe is

Card number 4 reading left to right top to bottom…

Reason

In all the other cards where ab+cd=ef, (axb)+(cxd)=(exf)…

In card

4 however (2x9)+(5x7)=53 but 8x6=48…

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    $\begingroup$ I suppose one could check that the 11 special flip cards are indeed the only special flip cards but that is only interesting if there is a reasonably clever argument to show it instead of just bashing out all the cases. $\endgroup$ Commented Jul 29, 2025 at 6:59
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I found a different odd one out...

The card is 16 19 35

Reason

If each card is AB+CD=EF, the formula is (A+B+1)%10+C+D=E+F

Though all 12 match a similar rule

I thought the rule was A+B+C+D-9 = E+F but actually all 12 follow that rule. It only works if you discard the number if A+B is less than 10

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  • $\begingroup$ Welcome to Puzzling Stack Exchange, take our tour. Personally, I prefer the other answer because it doesn't have to introduce the modulus operator or any extra constants. $\endgroup$ Commented Jul 29, 2025 at 22:41
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    $\begingroup$ There are two problems with this answer: Addition commutes, but AB and CD are treated differently, and there are more cards satisfying your rule than the 11 you think are real. $\endgroup$ Commented Jul 30, 2025 at 0:18

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