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Problem of the Week

Problem D and Solution

Doing Some Beading

Amir is putting beads on a string. He plans on starting with 8 round beads, then 24 square beads, then 48 round beads, and then \(p\) square beads (where \(p>0\)). At some point after he has put on \(n\) beads (where \(n>0\)), he realizes that on his string there are twice as many beads of one shape than there are of the other shape. Determine the maximum and minimum values of \(p\) that result in exactly 5 possible values of \(n\).