# What is the number in the square with “?”?

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.

• Do you not know the answer? – Gordon Allocman May 23 '16 at 0:50
• You should clearly mention the source (book name, web-link etc) – Mohit Jain May 23 '16 at 5:14
• @GordonAllocman I know the answer now. – Wei-Cheng Liu May 23 '16 at 12:02
• @MohitJain I don't know the source. My wife borrowed her mobile phone to me and asked me to solve this IQ test. – Wei-Cheng Liu May 23 '16 at 12:03
• 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. :) – Ian MacDonald May 24 '16 at 17:01

98

Reason

flipped first column = middle column - last column

eg:

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

• 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. – Peregrine Rook May 23 '16 at 6:52
• Oops, Its column, thanks for the edit and suggestions :) – renji May 23 '16 at 7:04
• Yay, now I feel like a smart guy. – IllidanS4 wants Monica back May 23 '16 at 13:21

85
Horizontal sums are divisible by 3. Only 85 fits

$78$

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: $$(-35 * 18 - 247 * 17 + 10523) / 73$$

• You could do this for any possible answer, because there are three parameters (two coefficients and the constant term) and only two constraints. – f'' May 23 '16 at 7:54
• 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. – Mohit Jain May 23 '16 at 8:07
• @MohitJain I think that the purpose of this kind of "IQ test " question is to find a solution as short and natural as possible – Fabich May 23 '16 at 10:07
• @Lordofdark You are right. I lost the spirit a little early :( – Mohit Jain May 23 '16 at 12:06

I got the correct answer, but I did it a different way