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This is a brainteaser that I got from a friend.

Image

The question is what formula is being used in the cells?

If you take a closer look at the picture you will see that i = mod10((p or q)-1) and j = integer(i/10). I have also found out that this formula is used some how: a(n) = n^2+1.

But how is n generated? If you take a look at cell I31, why is n = 1.41421356 there and not an integer? Am I thinking wrong?

Any clues would be appreciated.

Link to larger image: http://i.stack.imgur.com/oaHcY.jpg

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    You should link if possible to a larger image. This is hard to read on my 2560x14440 monitor.2011-11-16
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    Sorry, here is the link: http://i.stack.imgur.com/oaHcY.jpg2011-11-16
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    For what it's worth, 1.41421356 is $\sqrt2$.2011-11-16
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    So for every ten values they take another degree of root, first is the first degree, then the second, then the third and so on?2011-11-16
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    @David your monitor is six times as tall as it is wide?2011-11-16
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    oops, an extra 4 there :)2011-11-16
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    Not too hard once you spot the three obvious square roots ($1.414214,2.236068$, and $3.162278$) and start squaring the other entries.2011-11-16
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    I was missing the the second square... Did +1 instead and nothing worked. Solved now thanks to Chris.2011-11-16

1 Answers 1

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For cell $(p,q)$ you generate

$$i(p)=(p-1)\bmod 10$$ $$j(p)=\left\lfloor\frac{p-1}{10}\right\rfloor$$

Then the value in cell $(p,q)$ is

$$a(p,q) = \sqrt{(j(p) - j(q))^2 + (i(p) - i(q))^2}$$