# 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? Aug 9, 2018 at 12:00
• no. they were random Aug 9, 2018 at 12:02
• Oh... then my answer is probably not correct... I haven't looked at @jafe 's just yet. Aug 9, 2018 at 12:03

17+29=43

Because

All numbers are presented in base-13

• – Bass
Aug 9, 2018 at 11:02
• you got it, it was pretty obvious i suppose @jafe Aug 9, 2018 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 $$A and $$\max\{A,B\} = B$$ if $$B.

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. Aug 9, 2018 at 12:07
• @ShahriarMahmudSajid If $4+5=9$, would $5+4=9$? (In your puzzle, I mean.) Aug 9, 2018 at 12:08
• yes, it would . Aug 9, 2018 at 12:11
• @ShahriarMahmudSajid I looked at jafe's answer. Facepalm. Aug 9, 2018 at 12:16
• ha ha, simplest answer was the right answer here.. Aug 9, 2018 at 14:48