There are three gods: A, B, and C. One of them always tells the truth, one always lies, and one answers randomly. You can ask them three yes-or-no questions to determine which god is which. However, they will answer in their own language, where "yes" and "no" are represented by "da" and "ja", but you don't know which means which. What questions do you ask to figure out who is who?

The language barrier can be neutralised: think of a question whose answer you already know, so that "da" and "ja" reveal themselves regardless of which means which.

Your first priority is to find a god who is definitely not Random — once you have a reliable interlocutor, the rest follows.

You are in a room with two doors. One door leads to freedom, and the other leads to certain death. There are two guards, one in front of each door. One guard always tells the truth, and the other always lies. You can ask one guard one question to determine which door leads to freedom. What do you ask?

If you ask "are you the lying guard?" both guards give the same answer. If you ask "are you the truthful guard?" both guards also give the same answer. You need to think of a question that will yield the same answer from both guards, but that also gives you the information you need to choose the correct door.

Four people need to cross a bridge at night. They have 17 minutes before the bandits chasing them will catch up and cut the bridge's ropes. They have one flashlight, and the bridge can only hold two people at a time. Each person walks at a different speed: Person A takes 1 minute to cross, Person B takes 2 minutes, Person C takes 5 minutes, and Person D takes 10 minutes. When two people cross together, they must go at the slower person's pace. Can they cross the bridge in time?

The naive approach — always send the fastest person back with the flashlight — takes 19 minutes. The saving comes from how you handle the two slowest people.

A farmer needs to cross a river with a wolf, a goat, and a cabbage. He has a boat that can only carry himself and one other item. If he leaves the wolf alone with the goat, the wolf will eat the goat. If he leaves the goat alone with the cabbage, the goat will eat the cabbage. How can the farmer get all three across the river safely?

The farmer is allowed to bring items back across the river.

You take 2 essential medications daily, but you've mixed up the pills. You have 2 A pills and 2 B pills in a pile. The pills look identical and weigh the same amount. How can you ensure you take the correct dose for the next 2 days?

Think about what you could do to every pill in the pile such that you end up with exactly the right amounts each day, without needing to tell them apart.

You have three boxes: one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes are labeled, but all the labels are incorrect. You can only open one box and take out one piece of fruit to determine which box is which. Which box do you open, and what do you take out to figure out the correct labels?

Since every label is wrong, you know for certain that the box labeled "apples & oranges" contains only one type of fruit. Start there.

You have two wicks of different lengths. Each wick takes exactly one hour to burn completely, but neither burns at a constant rate (e.g. one wick might burn its first half quickly and the second half slowly). How can you measure 45 minutes using these two wicks?

You're not restricted to lighting a wick from one end only.

Four men are lined up, one behind the other, with a wall separating the first man from the remaining three:

The men know that two of them are wearing red hats and two are wearing blue hats. They can see the hats in front of them but not their own hat or the hats behind them. No one can see the colour of the hat worn by the man standing past the wall. They aren't allowed to communicate. Which man can figure out the colour of his own hat, and how?

A person not claiming their hat colour is itself useful information — think about what they would have had to see in order to know.

You have 12 coins, and one of them is counterfeit. The counterfeit coin is either heavier or lighter than the genuine coins, but you don't know which. You have a balance scale that you can use three times. How can you determine which coin is counterfeit and whether it is heavier or lighter?

Each weighing has three possible outcomes (left heavy, right heavy, balanced). Three weighings give you at most 27 outcomes — enough to distinguish between 24 possibilities (12 coins × heavier or lighter).

Your first weighing should leave some coins unweighed — coins you know are genuine can be used as a reference in later weighings.

Pirates must divide 100 gold coins. The most senior proposes a split; if 50% or more approve it passes, otherwise he's thrown overboard and the next takes over. What does the senior pirate propose?

Work backwards: start with just two pirates and figure out what happens, then build up to three, four, and five.

A pirate will accept any offer that's strictly better than what they'd receive if the proposal fails — even just one coin more.