The coin problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that asks for the largest monetary amount that cannot be obtained using only coins of specified denominations. For example, the largest amount that cannot be obtained using only coins of 3 and 5 units is 7 units. The solution to this problem for a given set of coin denominations is called the Frobenius number of the set.
There is an explicit formula for the Frobenius number when there are only two different coin denominations. If the number of coin denominations is three or more, no explicit formula is known; but, for any fixed number of coin denominations, there is an algorithm computing the Frobenius number in polynomial time (in the logarithms of the coin denominations forming an input). No known algorithm is polynomial time in the number of coin denominations, and the general problem, where the number of coin denominations may be as large as desired, is NP-hard.
Read more about Coin Problem: Statement, Frobenius Numbers For Small n
Famous quotes containing the words coin and/or problem:
“It is not funny that a man should be killed, but it is sometimes funny that he should be killed for so little, and that his death should be the coin of what we call civilization.”
—Raymond Chandler (1888–1959)
“The problem of culture is seldom grasped correctly. The goal of a culture is not the greatest possible happiness of a people, nor is it the unhindered development of all their talents; instead, culture shows itself in the correct proportion of these developments. Its aim points beyond earthly happiness: the production of great works is the aim of culture.”
—Friedrich Nietzsche (1844–1900)