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Let's have the following numbers.

$(5i+\frac{1}{2})$, $(2i+3)$, $(\frac{-101}{8})$, $(7i+4)$, $(5i+1)$, $\frac{(40i-97)}{8}$.

How are these numbers related when taken three at a time? Operations allowed + - x ÷ ^

HINT: The three numbers, when chosen correctly, will solve this equation: $x^3=a^2-b^2$

There is only one solution.

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    $\begingroup$ This looks to be another "guess what I'm thinking" problem. Three are probably infinitely many relationships one could draw. $\endgroup$ – bobble Mar 1 at 0:27
  • $\begingroup$ When the numbers are chosen correctly, three at a time, (no more than three numbers) there is only one answer. $\endgroup$ – Vassilis Parassidis Mar 1 at 0:32
  • $\begingroup$ That's not a hint, it's the problem statement. Without telling us what equation to solve, this isn't a puzzle. It's a guessing game. $\endgroup$ – bobble Mar 1 at 2:27
  • $\begingroup$ @ bobble. Choose the three numbers with denominators then you can answer the question. $\endgroup$ – Vassilis Parassidis Mar 1 at 2:41
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I'm not sure if this is what you were thinking but here is one possibility

$(2i+3)+(5i+1)+\frac{(40i-97)}{8} = \left(5i+\frac{1}{2}\right) + (7i+4) + \left(\frac{-101}{8}\right)$

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  • $\begingroup$ Your answer uses six numbers not three at a time. $\endgroup$ – Vassilis Parassidis Feb 28 at 23:58
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    $\begingroup$ Three on the left, three on the right. $\endgroup$ – Gareth McCaughan Mar 1 at 0:53
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    $\begingroup$ If you meant e.g. "what relation holds between my first three numbers and also between the other three numbers?" then you should have said that. But it would still have been a "guess what I'm thinking" puzzle. $\endgroup$ – Gareth McCaughan Mar 1 at 0:54
  • $\begingroup$ As stated in the question, take three number and using these three numbers, find a solution. $\endgroup$ – Vassilis Parassidis Mar 1 at 1:24

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