TITLE: Given two blank rulers, measure any length
QUESTION [23 upvotes]: Say, you are given ruler $A$ of length $72.84 \text{ cm}$ and ruler $B$ of length $86.63\text{ cm}$. Neither of them have any marking/gradation of any sort on them. They are blank, except for their total length written on them.
Using only A and B, can you measure a length of $31.23\text{ cm}$?
Also, is it possible to generalize this concept further?
That is to say:

Given any two blank rulers, measure any given length.

REPLY [8 votes]: The other answers are in the affirmative and consider measuring multiples of the GCD of the two rulers, or $0.01\text{ cm}$ in the original problem.
For really small problems, it would be better to have an irrational ratio between the two lengths, e.g. a ruler of length $1$ and a ruler of length $\pi$. One can get multiples of $\pi$ arbitrarily close to the integers and thus construct basic units of measurement arbitrarily small.
Doing so, you can measure ANY non-negative real length to ANY desired positive degree of accuracy. Contrast such a ruler with the $0.01\text{ cm}$ ruler mentioned above which can only measure any non-negative real within $0.01\text{ cm}$ of accuracy ($0.005$ really, but there's an uncertainty in the measurement in which side it is actually closer to, so you wind up with up to $0.01$ from the further side).