Given cents of value $p_1,p_2,p_3,\cdots ,p_n$. Aim is to find minimum value of $x$ such that for all $y>=x$, there exists a combination of given cents denomination that adds upto $y$. All $p_i$'s are positive integers.

For $n=2$ and numbers of the form $k,k+1,k(k-1)$ seem to work good but can we prove if it is the minimum possible, i tried using induction but got stuck at the inductive step.



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