Question

Box of oranges*
Three travelers arrive late at night at the inn, but the kitchen is already closed. The innkeeper mutters: all I have is a box of old oranges... The travelers say that is fine since the alternative is no food at all. The innkeeper disappears and the three travelers have fallen asleep by the time he comes back. The innkeeper does not want to wake the travelers so he leaves the box on the table and goes to bed.
The first traveler wakes up and finds the box of oranges. Not wishing to make a pig of himself and not knowing if anyone else has eaten something already, he throws away one orange that looks bad and eats a third of what is left. He goes back to sleep.

The second traveler wakes up. This traveler wants to be fair too. He throws out two ugly, dried out oranges, eats a third of what remains and goes back to sleep.
The third traveler wakes up. He throws out three half rotten oranges and eats a third of what remains.

It is almost morning and the innkeeper returns and takes away the box. Only six left, mutters the innkeeper.

Calculate how many oranges there were in the box to start with? Motivate your answer and explain which strategy you have used.

Answer 1