MathDB

For positive integers

a

b

, and

c

with

a < b < c

, consider collections of postage stamps in denominations

a

b

, and

c

cents that contain at least one stamp of each denomination. If there exists such a collection that contains sub-collections worth every whole number of cents up to

1000

cents, let

f(a, b, c)

be the minimum number of stamps in such a collection. Find the sum of the three least values of

c

such that

f(a, b, c) = 97

for some choice of

a

and

b

Problem Statement