Can you pay 1 million using half a million bills?
In a certain country, banknotes are of four types: 1 dollar, 10 dollars, 100 dollars, and 1000 dollars. Can you pay an amount of one million dollars using exactly half a million bills?
NO, quantity = quantity : x + y + z + w = 500,000
money = money ; x + 10 y + 100 z + 1000w = 1,000,000
subtract 1st from 2nd ; 9 y + 99z + 999w = 500,000
left has a factor of 9 while the right does not..thus no integer solutions exist
