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Orange Poster, Question 4

Three customers are charged €30 between them for their pizzas. They give the waiter €10 each and when he gets to the till he is told that the bill should be €25 and he is give 5 €1 coins change. Unable to divide €5 by 3 he gives the customers €1 each and slips €2 into his pocket. So the customers page €9 each that's €27 and the waiter has €2 - that's €29 where is the missing euro?

Answer:

This is a REALLY NASTY one! It made my brain sore when I first heard it. Of course, there is no money missing. There was €30 put in the till and €5 taken out. There’s no money missing there! Of the €5 taken out, €3 was given back to the customers and €2 kept by the waiter: still no money missing.

 

The way the question was phrased confuses us. Though it sounds plausible, you can’t add what the customers paid, with what the waiter keeps. You can add what everyone has at the end of the transaction.

We should phrase it like this – the customers paid €27 and the waiter keeps €2, which means the restaurant gets €25. So we should subtract the €2 to get down to the amount in the till. But, it is still not clear why the way the question is phrased is faulty. There is a lot of misdirection in the question.

The question could be changed to have the customers give a tip of €2, which doesn’t change any calculation. But, somehow the waiter pocketing €2 is an extra distraction for us. Incidentally it could also be just one customer tendering €30 for a €25 meal. Try it like this –

A customer is charged €25 for a meal in a restaurant. She gives the waiter €30. The waiter comes back with €5 change and the customer gives her €2