Top Qs
Timeline
Chat
Perspective

Postage stamp problem

From Wikipedia, the free encyclopedia

Postage stamp problem
Remove ads

The postage stamp problem (also called the Frobenius coin problem and the Chicken McNugget theorem) is a mathematical riddle that asks what is the smallest postage value which cannot be placed on an envelope, if the latter can hold only a limited number of stamps, and these may only have certain specified face values.[1]

Thumb
13 is the smallest total that cannot fit on an envelope with space for only three stamps of possible values 1, 2, 5 and 20

For example, suppose the envelope can hold only three stamps, and the available stamp values are 1 cent, 2 cents, 5 cents, and 20 cents. Then the solution is 13 cents; since any smaller value can be obtained with at most three stamps (e.g. 4 = 2 + 2, 8 = 5 + 2 + 1, etc.), but to get 13 cents one must use at least four stamps.

Remove ads

Mathematical definition

Mathematically, the problem can be formulated as follows:

Given an integer m and a set V of positive integers, find the smallest integer z that cannot be written as the sum v1 + v2 + ··· + vk of some number km of (not necessarily distinct) elements of V.

Complexity

This problem can be solved by brute force search or backtracking with maximum time proportional to |V |m, where |V | is the number of distinct stamp values allowed. Therefore, if the capacity of the envelope m is fixed, it is a polynomial time problem. If the capacity m is arbitrary, the problem is known to be NP-hard.[1]

See also

References

Loading related searches...

Wikiwand - on

Seamless Wikipedia browsing. On steroids.

Remove ads