Disclaimer: This is a simplified part of a question from my homework, addressing the point that I didn't figure out.
let A be a 1-indexed sorted array of $n$ elements.
There are at most 3 numbers that has at least $\lfloor n/4 \rfloor+1$ occurrences.
Find three indexes that will surely "hit" all such numbers. Explain why it's certain.
Because this is a sorted array, all such numbers will be stacked together, so each "number group" have a limited freedom to travel around the array.
It feels like going symmetrically for $n/4$, $n/2$ and $3n/4$ would be a wise guess, but I'm not sure how to prove it, and furthermore $n$ might not be a multiplicity of 4, so we have to round up or down the indexes.
How can I tackle such question?