$4+5=9$
$7+9=13$
$11-5=9$
$17+29=\,?$
Find the value of "?"
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asked Aug 9, 2018 at 7:00
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$\begingroup$ Is the order of equations deliberate? $\endgroup$– Mr PieAug 9, 2018 at 12:00
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$\begingroup$ no. they were random $\endgroup$– Shahriar Mahmud SajidAug 9, 2018 at 12:02
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$\begingroup$ Oh... then my answer is probably not correct... I haven't looked at @jafe 's just yet. $\endgroup$– Mr PieAug 9, 2018 at 12:03
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2 Answers
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The answer is
17+29=43
Because
All numbers are presented in base-13
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2$\begingroup$ relevant: en.wikiquote.org/wiki/Talk:Douglas_Adams#Unsourced $\endgroup$– BassAug 9, 2018 at 11:02
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$\begingroup$ you got it, it was pretty obvious i suppose @jafe $\endgroup$ Aug 9, 2018 at 12:04
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Partial Answer
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?
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$\begingroup$ interesting attempt. but it was quite simple actually, you took it to be more difficult than it was. $\endgroup$ Aug 9, 2018 at 12:07
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$\begingroup$ @ShahriarMahmudSajid If $4+5=9$, would $5+4=9$? (In your puzzle, I mean.) $\endgroup$– Mr PieAug 9, 2018 at 12:08
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$\begingroup$ @ShahriarMahmudSajid I looked at jafe's answer. Facepalm. $\endgroup$– Mr PieAug 9, 2018 at 12:16
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$\begingroup$ ha ha, simplest answer was the right answer here.. $\endgroup$ Aug 9, 2018 at 14:48