June 2013 Logic & Maths Puzzles

1. Three men check their hats at the theatre, but the attendant mixes up the checks as she hands them out.

When the three men return after the performance to claim their hats, what is the chance that all three will get the correct hat back?

2. Three models – Ms Pink, Ms Green and Ms Blue – are on the cat-walk. Their dresses are solid pink, solid green and solid blue.

“It’s strange”, Ms Blue remarks to the others. “We are named Pink, Green and Blue, and our dresses are pink, green and blue, but none of us is wearing a dress that matches our name”.

“That is a coincidence”, agrees the woman in green.

Match each model to the colour dress she is wearing.

3.

If four apples plus three bananas plus two oranges cost \$1.60

Three apples plus two bananas plus two oranges cost \$1.26

One apple plus three bananas plus three oranges cost \$1.26

What is the total cost of one banana plus one orange plus one apple?

4.

At a business meeting each person shook hands with every other person exactly once. There were fifteen handshakes

How many people attended the meeting?

5.

Two ladies played cards for lollies. The winner received one lolly per game from the loser. When it was time to pack up, one lady had won three games, while the other lady had won three new lollies.

How many individual games had they played?

6. A man has four cards in his hand facing him.

He wants them placed in ascending order 2 to 5 from his left to his right (or, first to last). To do this, he takes the leftmost card and puts it last. He then takes the third card from the right and puts it in last place.

What was the previous order of the cards, left to right?

7. If you take a deck of 52 playing cards;

Shuffle them;

Deal them to yourself one at a time;

What is the least number of cards that must be dealt in order to be certain of    getting at least one four-of-a-kind?

8. If you then take two decks of 52 playing cards each;

Combine them;

Shuffle them;

Deal them to yourself one at a time;

What is the least number of cards that must be dealt in order to be certain of       getting at least one four-of-a-kind?

9. A census caller knocks on the door. A man answers.

The conversation goes as follows.

CENSUS TAKER: Good Evening sir, may I ask who lives here?

MAN: Myself and my three daughters.

CENSUS TAKER: And how old are your daughters?

MAN: The product of their ages is 72, and the sum of their ages is my house number.

CENSUS TAKER: I’m sorry, that’s insufficient information.

MAN: My eldest daughter really likes chocolate.

CENSUS TAKER: Thank you.

How old are the three daughters, and what is the house number?

10.

Alec, Bill and Charlie each work for a lawn-mowing concession.

Alec and Charlie are equally energetic, so that if they are hired individually to mow a certain sports ground, it will take each of them four hours, but will only take two hours if they work together.

Charlie is a bit lazy. If he is used as the third mower to mow the sports ground simultaneously the job time is reduced again, but only to one and a half hours.

Assuming Charlie works at a steady pace, how  long would it take him to mow the sports ground on his own?

SOLUTIONS HERE