A Fork in the Road

Should we go right or left?

Suppose there are two trolls at this fork in the road. One always tells the truth and the other always lies but you don’t know which is which. You have only one gold coin to pay one of them to answer a question. What question will you ask one of them to be 100% sure of which fork to take?

Here’s a much harder variation: You are lost in a country in which one third of the inhabitants always lie. The other inhabitants tell the truth, but only three quarters of the time. Desperate to get out of the country, you come to a fork in the road guarded by a troll. One way leads out and the other to certain death, but you don’t know which is which. You can ask the troll which way is out if you pay him a gold coin. You have four gold coins.

1. You pay the troll a gold coin and he advises you to go right. Does that answer help you to decide?

2. You pay the troll another gold coin and he advises you to go right again. Does that answer help you to decide?

3. You pay the troll another gold coin and he advises you to go right yet again. Does that answer help you to decide?

4. You pay the troll your last gold coin and he advises you to go left this time. You must make a final decision. What should you do?

5. What is the chance you get out of this country alive after you’ve paid your last gold coin?

Solutions can be found here.