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Juan must pay 4 bills and goes to an ATM

Source: Chile Finals 2013 L2 p6

October 5, 2022
combinatoricsnumber theory

Problem Statement

Juan must pay 44 bills. He goes to an ATM, but doesn't remember the amount of the bills. Just know that a) Each account is a multiple of 1,0001,000 and is at least 4,0004,000. b) The accounts total 200,00000, 000. What is the least number of times Juan must use the ATM to make sure he can pay the bills with exact change without any excess money? The cashier has banknotes of 2,0002, 000, 5,0005, 000, 10,00010, 000, and 20,00020,000. Juan can decide how much money he asks the cashier each time, but you cannot decide how many bills of each type to give to the cashier.
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