Find the missing number in these grids. I was unable to find any pattern.

3 grids of 5 cell


  1. 9
  2. 6
  3. 8
  4. 4

source: Borhan Motevasete magazine, Oct. 2007


Edit: Changed the reasoning based on Jaap Scherphuis's comment as it seems more natural.

I think the answer is



Add the numbers in the lower four boxes and take the absolute difference between the digits in the result to the get the number at the top (Originally: take the residue modulo $11$ to get the number at the top)


$4+1+6+3 = 14 \rightarrow |1-4| = 3$
$9+2+7+8 = 26 \rightarrow |2-6| = 4$
$3+1+8+5 = 17 \rightarrow |1-7| = 6$

  • 2
    $\begingroup$ The eleven seems a bit too arbitrary; there are only two samples, so if a modulus like that were allowed, almost any rule could be made to fit. $\endgroup$ – Bass Jul 15 '18 at 23:01
  • 1
    $\begingroup$ Slightly less arbitrary than mod 11 would be to take the difference of the two digits. It boils down to exactly the same thing since in all three cases the second digit is larger than the first. $\endgroup$ – Jaap Scherphuis Jul 16 '18 at 4:20
  • $\begingroup$ @JaapScherphuis Thank you, that's a good suggestion. $\endgroup$ – hexomino Jul 16 '18 at 8:43

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