One of my friend brought this simple-looking math puzzle to me, but it was harder than it seems. I tried several ideas including simple arithmetic operations, and even considering base-n.
5#2=18
8#2=11
7#4=45
3#5=33
6#3=?
The ?(answer) must be an integer.
I feel like this problem is underspecified, even if constrained by an obligation to find something terse (a point being made in the comments, I think).
For example, suppose we had a code phrase of "A CRY OF THE CRYPTOGRAPHER" (or in fact any phrase starting with "A CRY OF TH", and n#m meant to find the $n$th and $m$th letter (in "ACRYOFTHECRYPTOGRAPHER"), then translate them to numbers with $a=1, b=2, \ldots, z=26$, and finally add them up. That takes a while to write out, but is still pretty occam if I can shamelessly verb that (ugh, amiright?)
Anyway, that gives:
\begin{eqnarray} 5\#2&\rightarrow O,C \rightarrow 15+3 =& 18\\ 8\#2&\rightarrow H,C \rightarrow 8+3 =& 11\\ 7\#4&\rightarrow T,Y \rightarrow 20+25 =& 45\\ 3\#5&\rightarrow R,O \rightarrow 18+15 =& 33 \end{eqnarray}
So the answer is (okay, I'll put in a spoiler, but I can't believe that's what this is):
$6\#3\rightarrow F,R \rightarrow 6+18 = 24$
A little more on generating this solution (such as it is).
We have 2 small digits on the left, both less than 8. And we have 11 to 45 on the right. This range possibly suggests the sum of two letters, where letters are actually numbers from 1 to 26.
If this premise is correct (and I'm not saying it is, but it's at least conceivable), then we'd be looking for 8 letters to index against. Equations 1, 2, and 4, give us 10 possibilities:
-ap-q--j,-bq-p--i,-cr-o--h,-ds-n--g,-et-m--f,-fu-l--e,-gv-k--d,-hw-j--c,-ix-i--b,-jy-h--a,Equation 3 gives us 8 more possibilities:
---s--z----t--y----u--x----v--w----w--v----x--u----y--t----z--s-for a total of 80 possible templates, such as -cryo-th, which mixes the third of the first group (-cr-o--h) with the seventh of the second group (---y--t-). However, any of the 80 combinations would yield a valid solution. There are no one- or two-word solutions that fit (which would have been better, occam-wise I think), but there are many others that are a bit meh, but still work.
A couple of others:
The last of these translates as:
\begin{eqnarray} 5\#2&\rightarrow I,I \rightarrow 9+9 =& 18\\ 8\#2&\rightarrow B,I \rightarrow 2+9 =& 11\\ 7\#4&\rightarrow U,X \rightarrow 21+24 =& 45\\ 3\#5&\rightarrow X,I \rightarrow 24+9 =& 33\\ 6\#3&\rightarrow I,X \rightarrow 9+24 =& 33\\ \end{eqnarray}
Coincidentally, the same answer. "FIX XIX UBI" would have given us 48. Should I find one that gives an answer of 42?
