During the spring recruitment last year, I was quizzed by the interviewer on many intelligence questions. And I also just more interested in, so summed up a few more interesting, only for entertainment ~

It’s actually kind of funny if you think about it.

1. The problem of poison testing in mice

There are now 1000 bottles of potions, including 1 bottle of poison, which takes 1 hour to kill. We now have an hour to find the poison, so how many mice at least do we need to test it? Let’s say you have an infinite amount of water, you can dilute it indefinitely, and you don’t care how long you drink it.

Advanced problem

The poison is now altered and will act within 15 minutes. Other things being equal, how many mice are needed for an hour?

2. Round table shooters

There are numbers 1 through 1000 on the round table, number 1 on the right is number 2, and number 1000 on the left. One shoots two, gives the gun to three, three shoots four, gives it to five. And so on and so on, 999 kills 1000, hands the gun to 1, and then the cycle continues. What was the number of the last person left, please?

Advanced problem

Let’s say the number of peopleWhat was the last one to survive?

3. White hat problem

There are 100 students in one room. Everyone wears a hat on his head. The hat is white or black. Each student could only see the color of the other’s hat, but not his own.

The teacher said to everyone, “Each of you is wearing either a white hat or a black hat, and someone is wearing a white hat, please raise your hand.” If no one raises their hand, the teacher asks again a minute later, “Those in white hats, please.” The teacher then repeats the same question one minute at a time until all the students with white hats have raised their hands.

Let’s say every student is extremely smart, and only 5 out of 100 students wear white hats. Excuse me, at what time will all the students wearing white hats raise their hands?

Advanced problem

There was a town of 100 couples, and every husband was cheating on his wife. Wives can’t tell when their husbands are lying, but they can tell when any other man is lying. The law of the town forbade adultery, and the wife should kill her husband as soon as she proved him unfaithful, and all the women in the town had to strictly abide by this law. One day, a stranger suddenly arrives in town and declares that at least one husband has been unfaithful. So what happens next?

4. Pirate game

Five rational pirates (let’s just name them A-E) have found 100 gold coins and need to figure out how to divide them.

The principle is that the pirates propose A distribution plan from A to E. All the remaining pirates voted on whether to accept the proposal, including the proposer. More than half of the votes must be in favor of the proposal for it to pass, and then the gold pieces are distributed as proposed. If not, the proposer is thrown overboard and the next pirate comes up with a new allocation.

Now assume that the pirates are extremely smart, and their primary goal is to survive and get as much gold as possible. On top of that, they also tend to kill more people. What was their final result?

Advanced problem

Now, the condition for the bill to pass is that only half or more people need to support it, so what should be the outcome now?

5. Simply face the card problem

Assuming a total of 108 random cards are given to raccoons (with equal probability), what is the mathematical expectation of the number of packs that raccoons need to buy to collect all the cards?

Maybe you think these questions are boring… But someone might be interested. =

If you want answers and detailed explanations, go to: poison rats, round table shooter, white hat problem, pirate game problem