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I came across a puzzle in an exercise booklet for selective high school enrolment tests in Australia. The puzzle is shown in the picture below. Please help me work out the number in the cell marked by the question mark. Thank you very much. I just have no clue how these numbers are related to each despite looking at them in thoughts quite a while. enter image description here

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Pattern is:

2=16
3=14
4=?
5=10
6=8
(7=6)
8=4

So solution is:

12

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  • $\begingroup$ Thank you, Jan Ivan. I think that's the right pattern. You're so sharp-minded! $\endgroup$ – Michael May Nov 20 at 7:06
  • $\begingroup$ I arrived at the same solution but a different way. I saw the differences between consecutive top row numbers being +3 -2 +5 -2 -2, and the bottom row being -6 +4 -10 +4 X. So the bottom row differences were always -2 times the top row differences. Which makes the last difference +4, so 8+4=12. $\endgroup$ – JS1 Nov 20 at 9:28
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The answer is

12.

Solution

The trick here is about rearranging the order and analysing. Take the first row and rearrange it in the increasing order and at the same time, below to it, rearrange the second row in decreasing order:
first row-----second row:
2-----16
3-----14
4-----12
5-----10
6-----8
(7)-----(6)
8-----4

So for 4 its 12.

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