The paper is concerned with a sequential search on a finite set $X=F_1\cup F_2\cup\dots\cup F_n$ of coins, such that $|F_i|=5$; $i=1,2,\dots,n$; and $F_i\cap F_j=\emptyset$, for $i\neq j$. There is exactly one counterfeit (heavier) coin in each $F_i$ and we want to identify all of them. A weighing procedure is constructed for an arbitrary $n$, which implies an upper bound close enough to the theoretical lower bound.