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Placement Papers with Solutions

(#M40009155) SELF QUESTION Keep an EYE

Here is a puzzle known as the Covent Garden Problem, which appeared in London half a century ago, accompanied by the somewhat surprising assertion that it had mystified the best mathematicians of England:

Mrs. Smith and Mrs. Jones had equal number of apples but Mrs. Jones had larger fruits and was selling hers at the rate of two for a penny, while Mrs. Smith sold three of hers for a penny.

Mrs. Smith was for some reason called away and asked Mrs. Jones to dispose of her stock. Upon accepting the responsibility of disposing her friend's stock, Mrs. Jones mixed them together and sold them of at the rate of five apples for two pence.

When Mrs. Smith returned the next day the apples had all been disposed of, but when they came to divide the proceeds they found that they were just seven pence short, and it is this shortage in the apple or financial market which has disturbed the mathematical equilibrium for such a long period.

Supposing that they divided the money equally, each taking one-half, the problem is to tell just how much money Mrs. Jones lost by the unfortunate partnership?

Flower (13 years ago)

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(#M40009154) SELF QUESTION Keep an EYE

The hour and minute hands are at equal distance from the 6 hour, what time will it be exactly?

Flower (13 years ago)

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(#M40009153) SELF QUESTION Keep an EYE

On your travels you come to an old man on the side of the road holding three cards from a standard deck face down. Trying to make conversation you ask him what the three cards are.

He tells you, "To the left of the queen, are one or two jacks. To the right of the jack, are one or two jacks. To the right of the club, are one or two diamonds. To the left of the diamond, are one or two diamonds." What are the three cards?

Flower (13 years ago)

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(#M40009152) SELF QUESTION Keep an EYE

In two decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?

Flower (13 years ago)

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(#M40009151) SELF QUESTION Keep an EYE

A man has four cards in his hand facing him, from 2 to 5. He wants them placed in ascending order from his left to his right. To do this, he takes the leftmost card (from your perspective) and puts it last. He then takes the third card from the right (your right) and puts it in last place.

What was the previous order of the cards?

Flower (13 years ago)

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(#M40009150) SELF QUESTION Keep an EYE

Two ladies played cards for candy; the winner received one piece per game from the loser. When it was time for one of the ladies to go home, one lady had won three games, while the other lady had won three new pieces of candy.

How many individual games had they played?

Flower (13 years ago)

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(#M40009149) SELF QUESTION Keep an EYE

A blind-folded man is handed a deck of 52 cards and told that exactly 10 of these cards are facing up.

How can he divide the cards into two piles (possibly of different sizes) with each pile having the same number of cards facing up?

Flower (13 years ago)

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(#M40009148) SELF QUESTION Keep an EYE

Three people enter a room and have a green or blue hat placed on their head. They cannot see their own hat, but can see the other hats.

The color of each hat is purely random. They could all be green, or blue, or any combination of green and blue.

They need to guess their own hat color by writing it on a piece of paper, or they can write "pass".

They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.

If at least one of them guesses correctly they win $50,000 each, but if anyone guess incorrectly they all get nothing.

What is the best strategy?

Flower (13 years ago)

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(#M40009147) SELF QUESTION Keep an EYE

There are three Athletes (Alex, Brook and Chris) and their individual Coaches (Murphy, Newlyn and Oakley) standing on the shore.

No Coach trusts their Athlete to be near any other Coach unless they are also with them.

There is a boat that can hold a maximum of two persons.

How can the six people get across the river?

Flower (13 years ago)

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(#M40009146) SELF QUESTION Keep an EYE

At a restaurant, how could you choose one out of three desserts with equal probability with the help of a coin?

Bonus: What if the coin is biased and the bias is unknown?

Flower (13 years ago)

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