Once in a while an exam happens where nobody correctly solves (i.e. there might be partial solutions) that trivial problem of yours (and I'm not talking about intentionally hard and impossible tasks used, for example, in "testing waters").
First of all, it is my fault (i.e. when I wanted them to solve it and nobody did; it's another matter when I let students surprise me for bonus points). There are a lot of possible causes, e.g. an especially good day (like when everything seems simple), non-standard intuition, sometimes a missing dependency, like a formula from another course they should have known, but didn't (and I should have checked they do).
Question: However, after it happened, how one should grade such task? In particular, should the "maximum" be kept as intended, or maybe moved to progress point of the best solution?
Example: The task might be about throwing a fair coin some number of times, and bounding the number of obtained heads from below with given confidence. The basic solution could use the Chebyshev's inequality, but you can obtain a better bound with, for example, Chernoff bound.