Question 121
Currently circulating coins in Japanese currency come in 6 different denominations: 500 yen, 100 yen, 50 yen, 10 yen, 5 yen and 1 yen. Taro had 1 each of 1000 yen note, 100 yen coin, 10 yen coin and 1 yen coin. He made a certain purchase from a merchant and handed him all he had and received some change. Assume that Taro made the payment in such a way that he would not receive in the change any coins of the denominations same as what he had had to begin with, nor a 1000 yen note. Furthermore, he chose the method of the payment so that he would end up with the minimum possible number of coins when he received his change. Assume also that the merchant gave Taro the change with minimum possible number of coins. Count the case of no change as a possibility for the purchase price also. Under these conditions how many distinct purchase prices are possible?