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enter image description here

Original image here

Source: My coaching DPP (Daily Practice Paper)

A) $112$

B) $92$

C) $82$

D) $102$

I found $5^2+3^2-4^2=18,\,7^2+5^2-3^2=65.$ So, $?=8^2+6^2-5^2=75$ which is not in option. Anyone please help.

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  • 4
    $\begingroup$ This looks like a puzzle you found elsewhere. For content you did not create yourself, proper attribution is required. Can you please include the source for this puzzle? $\endgroup$ – hexomino Nov 8 at 14:32
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    $\begingroup$ What is a "DPP"? $\endgroup$ – Joel Reyes Noche Nov 8 at 15:02
  • $\begingroup$ it is 102 or 112 (intuition) $\endgroup$ – balazs.com Nov 8 at 15:44
  • $\begingroup$ Daily Practice Paper=DPP $\endgroup$ – Divya Prakash Sinha Nov 8 at 16:04
  • $\begingroup$ My guess, it should be multiple of 6 i.e. 102 $\endgroup$ – Divya Prakash Sinha Nov 8 at 16:05
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Since our dear friend balazs.com has not deigned to provide a comprehensible explanation to us lowly mortals, I've provided a simple explanation here:

The missing number is:

Not the only one missing

This is because:

You have correctly deduced the pattern for turning the outside numbers into the inside number. Specifically, the pattern adds the squares of the upper outside numbers and subtracts the square of the lower outside number to produce the inner number. As shown here:

 5*5 + 3*3 - 4*4 = 25 + 9 - 16 = 18
 7*7 + 5*5 - 3*3 = 49 + 25 - 9 = 65
 
The problem is that the third triangle is malformed per the available answer choices. The actual equation you're looking for is: 9*9 + 6*6 - 5*5 = 81 + 36 - 25 = 92. Therefore, the answer (central missing number) is B) 92, and the other missing number is 9, which should replace the misprinted 8 on the top left of the third triangle.

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  • $\begingroup$ I upvoted:) Much better! Sorry for laziness.. $\endgroup$ – balazs.com Nov 8 at 18:27
  • $\begingroup$ @balazs.com No problem, just try to write more in future :) $\endgroup$ – Avi Nov 8 at 18:27
  • $\begingroup$ I don't think assuming the puzzle itself is wrong is the right way. Otherwise every puzzle will be "wrongified" to suit our existing solution that coincidentally matches some examples. $\endgroup$ – ibrahim mahrir Nov 8 at 18:32
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    $\begingroup$ @ibrahimmahrir This is a pre-existing question with evidence of something changed in-between, not an original question. However, you are correct - it's normally not good to assume "wrongification". $\endgroup$ – Avi Nov 8 at 18:34
  • $\begingroup$ Sure, but there is a very blurry number in a very sensitive place. I found it a weird coincidence, but you still can be 49% right (very blurry - in the other picture, you have not seen that picture yet!) $\endgroup$ – balazs.com Nov 8 at 18:37
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it is 92 and there is a mistake on the picture;)

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  • $\begingroup$ You see, I told you, your solution is correct, we had to find the right question to it! And you did not believe me, rejected my edit:) $\endgroup$ – balazs.com Nov 8 at 16:42
  • $\begingroup$ The mistake being that an 8 has been printed instead of a 9... $\endgroup$ – Stiv Nov 8 at 16:43
  • $\begingroup$ I think you are right.Sorry for rejection as I thought it would spoil the question. $\endgroup$ – Divya Prakash Sinha Nov 8 at 16:44
  • $\begingroup$ No, I am just joking. Since I didn`t edit 8 to 9 but instead included E)75 as an option. (It was only a joke,sorry. But "there's a grain of truth in every joke") $\endgroup$ – balazs.com Nov 8 at 16:46
  • $\begingroup$ @balazs.com You earned a truly Explainer badge here :P (Edit the question and answer it... if you could edit the image :D) $\endgroup$ – Conifers Nov 8 at 17:02
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I suspect it is number

102, because the right number of the triangle divides the number inside the triangle and the other numbers don't have this property. As 6 divides 102 but not 82, 92,112 -> D) looks like the correct answer to me.

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