Just another simple math problem

$4+5=9$

$7+9=13$

$11-5=9$

$17+29=\,?$

Find the value of "?"

• Is the order of equations deliberate? – Mr Pie Aug 9 '18 at 12:00
• no. they were random – Shahriar Mahmud Sajid Aug 9 '18 at 12:02
• Oh... then my answer is probably not correct... I haven't looked at @jafe 's just yet. – Mr Pie Aug 9 '18 at 12:03

17+29=43

Because

All numbers are presented in base-13

• – Bass Aug 9 '18 at 11:02
• you got it, it was pretty obvious i suppose @jafe – Shahriar Mahmud Sajid Aug 9 '18 at 12:04

I will denote by a dot to represent multiplication for letters, in order to avoid confusion between $\times =$ times and $X=$ x.
(e.g. $A\times B = A\cdot B$).

I have found a pattern for the sums (+), but not the difference (-):

Let $\max\{A,B\} = A$ if $A>B$ and $\max\{A,B\} = B$ if $B>A$.
Let $\min\{A,B\} = A$ if $A<B$ and $\max\{A,B\} = B$ if $B<A$.

Then,

$$A+ B=\big(\min\{A,B\}\cdot (\max\{A,B\}+n)\big)-(\max\{A,B\}-1)^2+2-n$$

such that

$n$ represents the numbered equation it is. \begin{align}4+5&=9\tag{n=1} \\ 7+9&=13\tag{n=2} \\ 11−5&=9\tag{n=3} \\ 17+29&=\,\,?\tag{n=4}\end{align}

Therefore,

\begin{align}4+5&=4(5+1) - (5-1)^2 + 2 - 1 \\ &= 24-16 + 1\\ &= 9.\;\color{green}{\checkmark}\end{align} \begin{align}7+9&=7(9+2) - (9-1)^2 + 2 - 2\\ &= 77-64 + 0\\ &= 13.\;\color{green}{\checkmark}\end{align}

The pattern doesn't work for $11-5=9$ (because that has a minus instead of a plus), but if I am on the right track, this leaves the answer to be

\begin{align}17+29&=17(29+1)-(29-1)^2+2-4 \\ &= 510 - 784 - 2 \\ &= -276.\end{align}

Am I on the right track?

• interesting attempt. but it was quite simple actually, you took it to be more difficult than it was. – Shahriar Mahmud Sajid Aug 9 '18 at 12:07
• @ShahriarMahmudSajid If $4+5=9$, would $5+4=9$? (In your puzzle, I mean.) – Mr Pie Aug 9 '18 at 12:08
• yes, it would . – Shahriar Mahmud Sajid Aug 9 '18 at 12:11
• @ShahriarMahmudSajid I looked at jafe's answer. Facepalm. – Mr Pie Aug 9 '18 at 12:16
• ha ha, simplest answer was the right answer here.. – Shahriar Mahmud Sajid Aug 9 '18 at 14:48