# Find the missing number in the given puzzle

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.

• 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? Commented Nov 8, 2019 at 14:32
• What is a "DPP"?
– JRN
Commented Nov 8, 2019 at 15:02
• it is 102 or 112 (intuition) Commented Nov 8, 2019 at 15:44
• Daily Practice Paper=DPP Commented Nov 8, 2019 at 16:04
• My guess, it should be multiple of 6 i.e. 102 Commented Nov 8, 2019 at 16:05

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.

• I upvoted:) Much better! Sorry for laziness.. Commented Nov 8, 2019 at 18:27
• @balazs.com No problem, just try to write more in future :)
– Avi
Commented Nov 8, 2019 at 18:27
• 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. Commented Nov 8, 2019 at 18:32
• @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".
– Avi
Commented Nov 8, 2019 at 18:34
• 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!) Commented Nov 8, 2019 at 18:37

it is 92 and there is a mistake on the picture;)

• 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:) Commented Nov 8, 2019 at 16:42
• The mistake being that an 8 has been printed instead of a 9...
– Stiv
Commented Nov 8, 2019 at 16:43
• I think you are right.Sorry for rejection as I thought it would spoil the question. Commented Nov 8, 2019 at 16:44
• 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") Commented Nov 8, 2019 at 16:46
• @balazs.com You earned a truly Explainer badge here :P (Edit the question and answer it... if you could edit the image :D) Commented Nov 8, 2019 at 17:02

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.