Post Correspondence Problem - algorithm that solves the problem for a word with maximum K length
PCP is undecidable essentially because, if there is a match, it could be arbitrarily long. But, here, the question specifically excludes any string longer than $k$&nbsp;characters. There are only about $2^{k+1}$ possible strings of length at most&nbsp;$k$ over alphabet $\{a,b\}$. Does that help you find an algorithm?