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# Ants on a circle

Suppose n ants are placed on a circle with a diameter of one meter. Each ant location is chosen independently, uniformly at random. An ant chooses between clockwise or anti-clockwise direction, uniformly at random, and starts scampering along the circle. All ants move at the same speed: one meter per second. When two ants bump into each other, they reverse their direction of travel. One of the ants is named Alice. What is the probability that Alice returns to the same point as she started, one minute after the ants start their scampering?

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A newspaper made of 16 large sheets of paper folded in half. The newspaper has 64 pages altogether. The first sheet contains pages 1, 2, 63, 64.

If we pick up a sheet containing page number 45. What are the other pages that this sheet contains?

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3 / 111

A Lady (L) bought an item of Rs 100 from the Shopkeeper (C). She paid him through a 500 Rs Note. Realizing that he did not have change, the shopkeeper C got change for that note from another shopkeeper (S) and paid Rs 400 to the Lady. After a few days, S realized that the note is fake, And this railed at C and took 500 Rs back from him.

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So in this whole process how much money did C loose in the end?

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4 / 111

# Prisoner and Policeman

Policeman decided to punish the Prisoner and asked him to make a statement. The Prisoner should make such a statement so that he would be alive. If the statement is held true by Policeman, the Prisoner will be hanged to death and if the statement is held false, the Prisoner will be shot dead.

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# Muddy Heads

A mother tells her two children, a boy, and a girl, to play without getting dirty.

However, while playing, both children get mud on their foreheads.

The mother says At least one of you has a muddy forehead. She then asks the children to answer Yes or No to the question: Do you know whether you have a muddy forehead?

The mother asks this question twice.

What will the children answer each time this question is asked, assuming that a child can see whether his/her sibling has a muddy forehead, but cannot see his or her own forehead? Assume that both children are honest and that the children answer each question simultaneously.

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There is a guy in a boat holding a rope that's tight to a Top of the pole in the shore. He keeps pulling the rope until he reaches the shore. What is the speed relationship between the amount of rope he pulls, vs horizontal speed? Which speed is higher?

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A man is on an island, he doesn't know swimming, deep water is around the island and in water there are sharks & Crocodiles so if he goes in water they will eat him, there is fire broked in island he has to save himself, he is in east end and air is flowing from west to east direction and fire will reach east end within half-an-hour. How will he save himself?

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**Asked In :**Infosys8 / 111

**Monkey and Coconut Problem**5 person crash-landed on a beach. they collected few coconuts in a pile. as it was getting dark, they decide to divide it equally next morning. one person will take care of the coconuts. 1st person decided to divide the coconuts into equal parts and decided to hide his part. he then mixed the remaining coconuts into a pile but forgot 1 coconut, so he gave it to the monkey. next day, 2nd person also did the same.i.e. divided into equal parts, hid his part and gave 1 coconut to the monkey. what will be the minimum quantity of coconuts in the pile?

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**Asked In :**Infosys9 / 111

**Pirates of the Caribbean**Five pirates discover a chest full of 100 gold coins. The pirates are ranked by their ages. Pirate 5 is 50 years old, Pirate 4 is 49, and so on down to Pirate 1. To divide up the loot, they agree on the following:

The most senior pirate will propose a distribution of the booty. All pirates will then vote, including the most senior pirate, and if at least 50% of the pirates on board accept the proposal, the gold is divided as proposed. If not, the most senior pirate is murdered. Then the process starts over with the next most senior pirate until a plan is approved.

All Pirates are equally intelligent and selfish. Their preference is first to remain alive, and next to get as much gold as possible and finally, if given a choice between otherwise equal outcomes, to have fewer pirates on the boat.

Assume you are the senior most pirate in the group. Come up with a plan that maximizes your gold, and others will accept. How will you divide the coins?

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**Asked In :**Infosys10 / 111

**Prisoners Problem**There are 100 prisoners assigned by numbers in 1 to 100. Any number can be assigned to them. They need not be unique. They can talk one time before they assigned and they don't have any connection. Each one is requested to guess his number (they can use different strategies). He can see their numbers (but not their guess).

How can they do it so at least one of them guesses correctly his number?

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