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This is an IQ test I found recently. What is the number in the square with "?"? I have thought it for a long time but cannot know the answer. Does anybody know the answer and the reason? Thanks in advance.

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    $\begingroup$ Do you not know the answer? $\endgroup$
    – Gordon Allocman
    May 23 '16 at 0:50
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    $\begingroup$ You should clearly mention the source (book name, web-link etc) $\endgroup$
    – Mohit Jain
    May 23 '16 at 5:14
  • $\begingroup$ @GordonAllocman I know the answer now. $\endgroup$
    – Wei-Cheng Liu
    May 23 '16 at 12:02
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    $\begingroup$ @MohitJain I don't know the source. My wife borrowed her mobile phone to me and asked me to solve this IQ test. $\endgroup$
    – Wei-Cheng Liu
    May 23 '16 at 12:03
  • $\begingroup$ Trick question: there is no number in the square with the ?: the square has a ?. The question "which number should replace the ??" might have a different answer. :) $\endgroup$
    – Ian MacDonald
    May 24 '16 at 17:01
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98

Reason

flipped first column = middle column - last column

eg:

flipping 65, 56 = 69 - 13
flipping 14, 41 = 63 - 22
Hence ? will be 98

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    $\begingroup$ I believe that you mean "flipped first COLUMN = middle COLUMN − last COLUMN." P.S. As long as you're putting the answer in a spoiler block, do so consistently. $\endgroup$
    – Peregrine Rook
    May 23 '16 at 6:52
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    $\begingroup$ Oops, Its column, thanks for the edit and suggestions :) $\endgroup$
    – renji
    May 23 '16 at 7:04
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    $\begingroup$ Yay, now I feel like a smart guy. $\endgroup$
    – IS4
    May 23 '16 at 13:21
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85
Horizontal sums are divisible by 3. Only 85 fits

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The answer is:

$78$

The reason is:

If row elements are $a_1$, $a_2$ and $a_3$ from left to right: $$a_2 = (-35a_1 - 247a_3 + 10523) / 73$$ $69 = (-35 * 65 - 247 * 13 + 10523) / 73$
$63 = (-35 * 14 - 247 * 22 + 10523) / 73$
So the answer should be: $$(-35 * 18 - 247 * 17 + 10523) / 73$$

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    $\begingroup$ You could do this for any possible answer, because there are three parameters (two coefficients and the constant term) and only two constraints. $\endgroup$
    – f''
    May 23 '16 at 7:54
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    $\begingroup$ My plan was to say all four answers are correct. Then I got bored in proving first answer is correct. In short I don't find such questions appealing. $\endgroup$
    – Mohit Jain
    May 23 '16 at 8:07
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    $\begingroup$ @MohitJain I think that the purpose of this kind of "IQ test " question is to find a solution as short and natural as possible $\endgroup$
    – Fabich
    May 23 '16 at 10:07
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    $\begingroup$ @Lordofdark You are right. I lost the spirit a little early :( $\endgroup$
    – Mohit Jain
    May 23 '16 at 12:06
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I got the correct answer, but I did it a different way

Answer

98

My solution

The sum of the ones place digit in column one and the tens place digit in column three equals the tens place digit in column two, the sum of the tens place digit in column one and the ones place digit in column three equals the ones place digit in column two soo...

65 69 13 -- [5 + 1][6 +3] -- [6][9] = 69
14 63 22 -- [4 + 2][1 +2] -- [6][3] = 63
18 ?? 17 -- [8 + 1][1 +7] -- [9][8] = 98

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