MathDB

2

Part of 2004 Swedish Mathematical Competition

Problems(1)

100 coins in a bag in acountry where coins exist of 1,2,3,4 ,5.

Source: Swedish Mathematical Competition 2004 p2

3/21/2021
In one country there are coins of value 1,2,3,41,2,3,4 or 55. Nisse wants to buy a pair of shoes. While paying, he tells the seller that he has 100100 coins in the bag, but that he does not know the exact number of coins of each value. ”Fine, then you will have the exact amount”, the seller responds. What is the price of the shoes, and how did the seller conclude that Nisse would have the exact amount?
number theory