The question is:
The Riddler Manufacturing Company makes all sorts of mathematical tools: compasses, protractors, slide rules — you name it!
Recently, there was an issue with the production of foot-long rulers. It seems that each ruler was accidentally sliced at three random points along the ruler, resulting in four pieces. Looking on the bright side, that means there are now four times as many rulers — they just happen to have different lengths.
On average, how long are the pieces that contain the 6-inch mark?
I feel fairly confident about the answer, in part because the two methods gave me the same result. But given that I created both solutions, I wonder if I shouldn’t rate that fact too highly. If I’d created an analytic solution that matched someone else’s brute force solution, that might be more reliable.
One small issue with the rough brute force method is that it doesn’t account for a random cut on the six-inch mark; I’m not sure if that is even possible. Worse though, the random number generation method I chose can produce a zero, but not a one. The necessary adjustment for that would be miniscule, I assume, but it seems like a persistent source of bias. Of course, that bias will be drowned in the noise for any plausible number of trials.