(related to Problem: Giving Change)
The way to help the American tradesman out of his dilemma is this. Describing the coins by the number of cents that they represent, the tradesman puts on the counter $50$ and $25;$ the buyer puts down $100, 3,$ and $2;$ the stranger adds his $10, 10, 5, 2,$ and $1.$ Now, considering that the cost of the purchase amounted to $34$ cents, it is clear that out of this pooled money the tradesman has to receive $109,$ the buyer $71,$ and the stranger his $28$ cents. Therefore it is obvious at a glance that the $100$-piece must go to the tradesman, and it then follows that the $50$-piece must go to the buyer, and then the $25$-piece can only go to the stranger. Another glance will now make it clear that the two $10$-cent pieces must go to the buyer because the tradesman now only wants $9$ and the stranger $3.$ Then it becomes obvious that the buyer must take the $1$ cent, that the stranger must take the $3$ cents, and the tradesman the $5, 2,$ and $2.$ To sum up, the tradesman takes $100, 5, 2,$ and $2;$ the buyer, $50, 10, 10,$ and $1;$ the stranger, $25$ and $3.$ It will be seen that not one of the three persons retains any one of his own coins.
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