# Looking for a pattern in a math riddle

Looking to find a pattern but no idea how:

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

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

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

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

• 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. – punctured dusk Jan 20 '14 at 20:52
• Thanks, what is it then? Is it cryptography? sorry if i posted it here. – alchemist Jan 20 '14 at 20:56

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 $$14\square 94=?$$

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