Puzzle At A Bar in France

Three friends decide to share a bottle of wine in a bar.

The bottle costs 30 francs.

When the time comes to pay, the friends each give the waiter 10 francs.

The waiter takes the money to the till. The bar owner tells the waiter to give the drinkers a 5-franc discount.

The waiter takes five 1-franc coins from the till and returns to the drinkers’ table.

As he approaches the table he discreetly slips 2 francs into his pocket.

He then gives one of the remaining franc coins to each of the three friends.

Question: how much has each drinker paid for the wine? Answer: 10 francs minus 1 franc received in change equals 9 francs.

How much did they pay in all? Three drinkers spending nine francs each gives a total of 9x3=27 francs.

To which we mustn’t forget to add the 2 francs in the waiter’s pocket.

27 francs plus 2 francs equals 29 francs.

But we started with 30 francs. Where is the 30th franc?

This story made me aware of the power of storytelling to distract listeners from hard mathematical facts. No wonder politicians love telling stories.

The technique here is to play on the listener’s need for consistency. The story starts small by focusing on what each drinker pays, i.e. nine francs. Then it progresses to a larger number by multiplying the nine by three to get 27. As the total is already growing, it feels natural to grow it some more by adding the two francs from the waiter’s pocket to reach 29.

But adding the two is not allowed from a mathematical perspective because the two are already included in the 27….

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