## February 2014 Logic & Maths Puzzles

1.

A rowboat carrying a cannonball is floating in a swimming pool.
The cannonball is thrown overboard into the pool.
Will the water level in the pool
(a) Rise?
(b) Fall?
(c) Stay the same?

2.
A player scores 75 with three darts, hitting a treble, a double and a single (no bulls).
Given that the three numbers that he hits add up to 35 and that the difference between the largest and smallest numbers is 14, how is is score made up?
Write your answer in the form Treble = _ , Double = _, Single = _.

3.

A jailer has more than 1000 prisoners to guard and has to seat them at meal times according to the following rules:
• Each table is to seat the same number of prisoners.
• The number at each table is to be an odd number.
The jailer finds that when he seats the prisoners:
3 per table, he has 2 prisoners left over.
5 per table, he has 4 prisoners left over.
7 per table, he has 6 prisoners left over.
9 per table, he has 8 prisoners left over.
But when he seats 11 prisoners per table, there are none left over.
How many prisoners are there?

4. Applying a certain mathematical rule;
If you start with 10, you end up with 12.
If you start with 19, you end up with 30.
If you start with 23, you end up with 38.
Work out what the rule is, then using that rule, answer:
If you start with 14, what number will you end up with?

5.
How many triangles are there in this diagram?

6.

The works picnic lunch is being catered with Chinese food.
There are cartons of special fried rice, cartons of chicken chop suey, and cartons of combination seafood.
Everyone gets their own carton of rice.
Each carton of chicken chop suey is shared between two people.
Each carton of combination seafood is shared between three people.
There is no waste and no leftovers.
A total of fifty-five cartons is supplied.
How many picnickers are there?

7.
A ball is dropped from a height of 81 metres. It vertically rebounds 2⁄3 of the way each time before coming to rest.
a. How high will the first rebound take the ball?
b. With which rebound will the ball first rise less than 10 m?
c. With which rebound will the ball first rise less than 1 m?
d. Assuming it comes to rest after rebounding less than 2 cm high, how many times does the ball make contact with the ground?

8.
This is a picture of a new kind of bus to operate in New York. It’s shown in the stationary position, but when it moves, will it move in direction A or direction B?

9.

A farmer buys a horse for \$60.
He sells it to his neighbor for \$70.
Then he discovers he could have made a better deal.
He borrows \$10 from his wife, and buys the horse back for \$80.
He then sells it to another neighbour for \$90.
How much money did he make?

10. Given that this diagram:

decodes to the word “CRAB”, decode the following two messages.

SOLUTIONS