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Buying a cat and getting the correct change...

Source: ToT 2003 SO-3

June 26, 2011
combinatorics unsolvedcombinatorics

Problem Statement

A salesman and a customer altogether have 19991999 rubles in coins and bills of 1,5,10,50,100,500,10001, 5, 10, 50, 100, 500 , 1000 rubles. The customer has enough money to buy a Cat in the Bag which costs the integer number of rubles. Prove that the customer can buy the Cat and get the correct change.
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