In the USA, there are coins of 1 cent, 5 cents, 10 cents, 25 cents, 50 cents and 1 dollar.
You can pay one dollar using either one coin (100), or two coins (50 + 50), or three (50 + 25 + 25), or four (25 + 25 + 25 + 25), etc.

What is the smallest number such that you cannot pay $1 with that many coins?

Given only the coins presented in the statement "In the USA, there are coins of 1 cent, 5 cents, 10 cents, 25 cents, 50 cents and 1 dollar.", the smallest natural number of coins that cannot equal one dollar is 77 coins.

Given all coins of US legal tender, the smallest number of coins that cannot equal one dollar, today, is 201. (The US has minted 20 cent, 3 cent, 2 cent and half-cent coins. Though discontinued and no longer in normal circulation, they remain legal tender). Still, the question of the problem does not ask for a number of coins that equals one dollar, rather it asks for the smallest number such that you cannot pay $1. With the inclusion of these coins of numismatic interest, there is no natural number solution.

Posted by Dej Mar on 2008-04-01 11:54:08