Finding lost bottle (algorithm problem)
This is a classical problem that I have previously seen framed as a puzzle rather than a CS question (with some fixed $n$ and fixed number of beakers), though I don't remember any source for it.

You can solve it as follows:
Number your bottles from $0$ to $n-1$, and label your beakers from $1$ to $\lfloor\log_2(n-1)\rfloor+1$ (the number of bits needed to represent numbers $0$ to $n-1$ in binary).

Now for every bottle, do the following: let $x$ be the label of the bottle. For every $i$ such that there is an $1$ at the $i$'th position in the binary representation of $x$, put a bit of that bottle's compound in beaker $i$.

Now after 10 days, the beakers which explode will exactly spell out the number of the explosive bottle in binary.