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Find the missing number, and show how you found it.

enter image description here

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closed as off-topic by F1Krazy, Rupert Morrish, Glorfindel, boboquack, SteveV Jan 18 at 0:45

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This looks like a puzzle you found elsewhere. For content you did not create yourself, proper attribution is required. If you have permission to repost this, please edit to include (at minimum) where it came from, then vote to reopen. Posts which use someone else's content without attribution are generally deleted." – F1Krazy, Rupert Morrish, Glorfindel, boboquack, SteveV
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Hi Mursaleen. What is the source of this puzzle? Please include it in the question. Also, please include the picture, not just a link to the picture. Thanks and happy puzzling! $\endgroup$ – eye_am_groot Jan 17 at 18:45
  • $\begingroup$ A friend send it to me. $\endgroup$ – Mursaleen Salroo Jan 17 at 19:16
  • $\begingroup$ The problem is undertermined. You can make the answer X by using the formula: 9(A + 2B + 5C - 15) + X*(-A+B-C+3). $\endgroup$ – Florian F Jan 19 at 12:55
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Let $A$ be the top number, $B$ be the left number, $C$ be the bottom number and $D$ be the right number. The pattern is:

$$2(A+B+C+D+AC+BD)-(A-B)+(D-C)$$

I don't have time to simplify it now, but I guess it looks less random in the way I have put it, and perhaps looks better to the eye. I might look back at this puzzle later in the day. But anyway, let's continue to finish off this answer.

So for the first one, we have:

$A=7$
$B=5$
$C=1$
$D=2$

So using our formula, we should get $63$:

$$2\times\big(7+5+1+2+(7\times 1)+(5\times 2)\big)-(7-5)+(2-1)=63$$

For the second one, we have:

$A=5$
$B=4$
$C=2$
$D=3$

So using our formula, we should get $72$:

$$2\times\big(5+4+2+3+(5\times 2)+(4\times 3)\big)-(5-4)+(3-2)=72$$

It works both times, so let us apply it to the third and final case. We have:

$A=4$
$B=3$
$C=1$
$D=2$

So using our formula, we get:

$$2\times\big(4+3+1+2+(4\times 1)+(3\times 2)\big)-(4-3)+(2-1)=40$$

However, none of the answers seem to be this... even though it works. Is it an error, or there might be a different formula. I am leaving this answer here as it is too long for a comment, and I can perhaps give others ideas to find an answer.

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