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 $$n$$.