Three travellers are on the road. As the day comes to an end, they pass through a village and agree they should stay here for the night. As luck would have it, the Brown Bear Inn is just down the road. They enter the building and ring a bell that is lying on the counter.

The innkeeper emerges from a room behind the counter. "Gentlemen!" he says. "What can I do for you?". The travellers explain that they would like to have a room for the night. They ask if it is okay to share a single room with the three of them, as this will be less demanding of their tight budget. "No problem! I'll give you our family room. It is 30 coins for one night". The travellers pay 10 coins each and go up to their room to rest.

A couple of minutes later, the innkeeper has a sudden realisation. It is not Sunday, as he thought, Monday has come already. This means that all rooms are a bit cheaper and that he has charged the travellers 5 coins too much. So he grabs five coins, goes up to their room, and knocks on their door. "Excuse me", he says, "I just realised I charged you a bit too much for your stay, I somehow thought it was the weekend still. Your room is five coins cheaper on a Monday, so I've come to bring you your money back".

The travellers appreciate the innkeeper's honesty, but face a minor issue. How are they going to divide these five coins between the three of them? They discuss briefly and come to the following solution: each of the travellers will get 1 coin back. The last two coins will be a tip for the innkeeper as a reward for his honesty. Everyone's a winner!

Q: The travellers have now each paid 9 coins, or 27 coins in total, and the innkeeper has 2. They started with 30 coins, but the total is now 3*9 + 2 = 29. Where has the last coin gone?

Not part of the riddle: This is an old riddle that we had to get our heads around in primary school back in the Netherlands. I've occasionally used it as a 'party trick' and found that some peers also have a hard time solving it (university graduates, believe it or not). I feel like this might be one of those riddles that is easier if you see it written down, like here, in stead of just being told. But since I'm not sure if this riddle is well known outside the old country, I thought I'd share anyway. :-)

P.S. since I'm pretty new here, I am not too familiar with the tags yet. These two seemed appropriate to me, but if you have any other suggestions, please let me know.

  • $\begingroup$ Too bad, your story was really good, even better than the duplicated puzzle. Welcome to puzzling.SE by the way! $\endgroup$ – xhienne Sep 4 '18 at 16:58

Definitely a classic riddle. Anyway here's the answer

The last coin hasn't gone anywhere. The 27 coins they finally paid plus the 3 coins given back equals the 30 coins they originally paid. The 2 coins kept by the innkeeper plus the price of 25 equals the 27 coins that were paid.


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