Well, the biggest problem with puzzles of this nature is that there's no unique solution. There are an infinite number of functions f(x,y) that fit with the three data points we've been given. There's no way to derive the "right" answer (being whatever answer the writer of the puzzle had in mind). Here's a solution I was able to find by Googling this problem. Perhaps it's "right" but it could just as easily both be wrong. The original text of this solution can be found
here, but the page is in Korean. Muddling through the Google Translated version, I believe the rule given there to be: starting at
x, sum up
y numbers. So, we'd have:
2 * 3 = f(2, 3) = 2 + 3 + 4 = 9
5 * 4 = f(5, 4) = 5 + 6 + 7 + 8 = 26
6 * 2 = f(6, 2) = 6 + 7 = 13
Leaving us with the solution of:
7 * 4 = f(7, 4) = 7 + 8 + 9 + 10 = 34
In general, the formula for this function would be:
\(\displaystyle \displaystyle f(x,y)=\sum _{k=x}^{x+y-1}k\)
