# Simple Arithmetic Puzzle 5. Or is it?

A fifth puzzle from the set!

\begin{align}3+4&=17\\2+5&=7\\3+1&=2\\2+1&=1\\4+2&=0\\3+6&=\,\,?\end{align}

Can you find the value of the question mark?

• The odd one out appears to be $2+5=7$ because that is the only correct equation, but that's all I can gather at this point in time. (I need to go to bed.) $\;$ Edit: Stuff it — I am working on this ;) – Mr Pie Jul 16 '18 at 15:02
• Am I just being unnecessarily pedantic or are others as uncomfortable as I am with this type of fake equation syntax? The real question here is not "what is the value of the question mark" but "What functional definition of '+' makes these equations work?" In which case, why not just write "Find a function f such that f(3,4)=17 etc"? – MattClarke Jul 18 '18 at 6:18
• @MattClarke because not everyone enjoys math; sometimes, people need things to be nice and simple ;) – Mr Pie Jul 19 '18 at 1:40

It's quite a bit higher than the rest, but I want to say the answer is

513

The formula being

AB - BA

All equations:

34 - 43 =  81 -  64 =  17
25 - 52 =  32 -  25 =   7
31 - 13 =   3 -   1 =   2
21 - 12 =   2 -   1 =   1
42 - 24 =  16 -  16 =   0
36 - 63 = 729 - 216 = 513

• (+1) Correct. I'll have to make the next one trickier as everyone here is so smart :) – TheSimpliFire Jul 16 '18 at 15:57

Here is a quick observation I made.

$$a+b:= \frac{a(a^2+b-1)}{2}-1$$

However,

This only works for the first two equations: $(a,b)=(3,4)$ and $(a,b)=(2,5)$

And

A quick glance at the answer above reveals that I am most likely not on the right track anyway...