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I can't find any logical relationship in this grid! Could someone help me, please?

\begin{array}{|c|c|c|}\hline 7 & 4 & 1 & 7\\ \hline 4 & 8 & 9 & 3\\ \hline 5 & 6 & 4 & ?\\ \hline 3 & 2 & 6 & 5\\ \hline \end{array}

and choices are:
A. 8
B. 6
C. 5
D. 4

This book is the source of the puzzle. The translation of its title is Enhancing the intelligence and educational ability of children and adolescents.

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    $\begingroup$ That's not quite what's meant by "citing the source". The point is that we need to know where the question comes from. While we're at it: do you have the permission of whoever made the puzzle to reproduce it here? $\endgroup$
    – Gareth McCaughan ♦
    Commented Jul 15, 2018 at 20:11
  • $\begingroup$ @GarethMcCaughan I understand, but I don't know anything about this puzzle. I just have this piece of the image. It has been circulated among some people and I don't know its origin. $\endgroup$
    – 01000110
    Commented Jul 15, 2018 at 20:22
  • $\begingroup$ Ah. Then I think we have to close it; sorry! (For all we know, it may be a copyright violation, which would be illegal; for all we know, it may be a still-ongoing competition, which we have a site-wide policy against.) $\endgroup$
    – Gareth McCaughan ♦
    Commented Jul 15, 2018 at 21:21
  • $\begingroup$ Putting this on hold for the reason described above. OP, if you do find out where it's from and establish that it's OK for it to be reproduced here, it can be reopened. (Apologies for the misleading close reason that will appear in a yellow box below the question; we have a very limited number of reason-descriptions and they don't really cover all the possibilities.) $\endgroup$
    – Gareth McCaughan ♦
    Commented Jul 15, 2018 at 21:24
  • $\begingroup$ This reminds me of number sticks. $\endgroup$
    – Mr Pie
    Commented Jul 16, 2018 at 0:36

3 Answers 3

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It is D because if the sum of the first two columns is 39 and so will the second two

Edit

It could be B too because then the sum of two adjacent columns would be increasing by one each time

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  • $\begingroup$ The sums of the first 3 columns are 19, 20, 20. Completing it as 19, 20, 20, 19 is just as logical as 19, 20, 20, 21. Which is what you said, but there should be a more definite answer. $\endgroup$
    – Florian F
    Commented Jul 15, 2020 at 7:39
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As a way of reiterating @VassilisParassidis' answer from another perspective, the puzzle is reminiscent of a "connect wall" puzzle of which there are many examples on puzzle SE (e.g. here, here, and here.)

The thing to note is that the 4x4 layout is not ordered in any particular way - the items could just as easily be given as an unordered list of 16 items. There are four groups of four items - your job is to identify them.

Adding up all the known numbers, you have $7 + 4 + 1 + \ldots + 5 = 74$. Unlike the items in the connect wall puzzles which are linked by word association, the connection here must be derived from the numbers. One idea is that the numbers in each group sum to the same number. Of the four options (8, 6, 5, and 4) only one of these when added to 74 results in a number which is divisible by 4, namely 6. So, each group sums to $(74 + 6)/4 = 20$.

To verify that this actually works, we just need to find four groups of numbers that sum to 20. i.e.:

enter image description here

(Note that these groups are not unique, but the option from the multiple choice list is - only B (6) will work.)

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The missing number is 6.

Inside the square we have 2,7-3,4-2,6-1,1-1,8-1,9-2,5-1,2-2,3. If we use all numbers taken four at a time regardless of combinations the missing number is always 6 when the sum of the four numbers is equal to 20.

6+4+6+4=20

7+7+4+2=20

8+3+3+6=20

9+5+5+1=20

More logical explanatios exist, but I prefer the one I gave above.

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    $\begingroup$ Even if OP indicated 2 was a possible answer, I have no idea where these eight equations of yours come from... $\endgroup$
    – Feryll
    Commented Jul 14, 2020 at 22:56
  • $\begingroup$ I changed my answer. The equations come from adding the numbers inside the square. $\endgroup$
    – Vassilis Parassidis
    Commented Jul 14, 2020 at 23:17
  • $\begingroup$ I think what @VassilisParassidis means is that the grand sum of the known number is 74. If there are four groups (like "connect wall" puzzles on SE) and they each add to the same (whole) number, then 6 is the only possible answer. $\endgroup$
    – Earlien
    Commented Jul 15, 2020 at 2:43
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    $\begingroup$ @Earlien I'm still not following. What 4 groups add to the same whole number in this puzzle? $\endgroup$
    – Cotton Headed Ninnymuggins
    Commented Jul 15, 2020 at 6:09
  • $\begingroup$ @CottonHeadedNinnymuggins I've added an answer to explain in greater detail. $\endgroup$
    – Earlien
    Commented Jul 15, 2020 at 7:13

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