3
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Looking to find a pattern but no idea how:

$12\mathop{\square}21 = 86$,

$13\mathop{\square}31 = 192$,

$14\mathop{\square}58 = 389$,

$14\mathop{\square}94 = \ ?$

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  • $\begingroup$ The fact that it's about numbers doens't mean it's about mathematics. Unless your friend asked you for a multivariate lagrange interpolation or something, but I bet he didn't. $\endgroup$ – punctured dusk Jan 20 '14 at 20:52
  • $\begingroup$ Thanks, what is it then? Is it cryptography? sorry if i posted it here. $\endgroup$ – alchemist Jan 20 '14 at 20:56
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This problem is not clearly defined. One of infinitely many ideas is the ansatz

$$x\square y := x\cdot a +b+ c\cdot y$$

leading to 3 equations, which can be solved giving

$$a=\frac{892}{17}, b=\frac{-11153}{17}, c=\frac{91}{17}.$$

Now, what is $$14\square 94=?$$

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  • 1
    $\begingroup$ The answer comes out to be $582+\frac{9}{17}$. Kind of skeptical about whether this is it though. $\endgroup$ – 2012ssohn Jan 20 '14 at 21:18
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    $\begingroup$ @2012ssohn Of course not! It's supposed to be in decimal form: 582.5294117647059... $\endgroup$ – Dustan Levenstein Jan 20 '14 at 21:20
  • $\begingroup$ Yeah, but it's symmetric: $582+\tfrac{9}{17}=\tfrac{9889}{17}$ $\endgroup$ – flonk Jan 20 '14 at 21:22
  • $\begingroup$ $\frac{9903}{17}$, actually. $\endgroup$ – 2012ssohn Jan 20 '14 at 21:24
  • 1
    $\begingroup$ @2012ssohn let's agree on $581.7058823529412...$ $\endgroup$ – flonk Jan 20 '14 at 21:32

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