Let see who can crack this.

Find the missing numbers in the image.

enter image description here

Explain the logic. Challenge for all masterminds

  • 3
    $\begingroup$ It's not a good puzzle because it looks like there could be many (infinitely many?) correct answers for it, as shown below. I tried to flag it as too broad, but it wouldn't let me because it has a bounty. $\endgroup$
    – JLee
    Jul 8, 2015 at 18:17
  • $\begingroup$ As there's a lot of support for this question being too broad, I've returned your bounty and closed the question. If you have any other details or information, feel free to edit it in to clarify what the answer should be. $\endgroup$
    – user20
    Jul 8, 2015 at 23:18
  • $\begingroup$ Maybe change to: provide proof that there are infinitely many solutions :) $\endgroup$
    – MarcelDevG
    Jul 9, 2015 at 9:43

4 Answers 4


The sum of numbers in the triangle is equal to the square of the number in the cirle. 4*4=6+8+x, 16=14+x, so x=2. The same routine for the rest

So the number are:

2, 5, 20, 23

But there could be a lot of other solutions....

  • $\begingroup$ An elegant solution! $\endgroup$ Jul 8, 2015 at 13:47

that follows a equation:-


Hence,the solution for missing,'?'s will be,




It's a lame solution but it works:



Number on top represents the minimum value in the triangle.


Here's a stab at it

First triangle: 3
Second triangle: 6
Third triangle: 14
Fourth triangle: 32

The number in the top circle forms an arithmetic progression with the upper two numbers (in the order: circle number, left triangle number, right triangle number). The lower triangle contains the common difference of the A.P. reversed in case if the C.D. is a two digit number, else if it is a one digit number we add 1 to the C.D.

  • $\begingroup$ Everything is OK. But the lower triangle...... There may be another answer.. $\endgroup$
    – apm
    Jul 4, 2015 at 6:46

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