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Problem of the Week
Problem E
Let’s All Ride a Bike

Grayson’s Groupcycles rents bikes with multiple seats for large groups of people. They rent \(7\)-seater, \(13\)-seater, and \(25\)-seater bikes. A group of \(14\) people could fit on two \(7\)-seater bikes, however a group of \(15\) people could not fit exactly on any of the bikes since no combination of bikes have exactly \(15\) seats.

What is the largest group size that cannot fit exactly on any combination of bikes from Grayson’s Groupcycles?