Problem of the Week 829

Coconut Counting

On a desert island, five students and a monkey gather coconuts all day, then sleep. The first student awakens and decides to gather her share. She divides the coconuts into 5 equal shares with one left over, gives the extra one to the monkey, hides her share, and goes to sleep. Later, the second student awakens and takes his fifth from the remaining pile. He, too, finds one extra and gives it to the monkey. Each of the three remaining students does likewise in turn. Find the minimum number of coconuts originally present.

Source: This problem appears in Birkhoff and Mac Lane, A Brief Survey of Modern Algebra, 2nd edition, p. 25.

© Copyright 1997 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998