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
It will be seen that not one of the three persons retains any
one of his own coins.