## June 2014 Logic & Maths Puzzles

1. A brother says of his younger brother:
“Two years ago I was three times as old as my brother was. In three years’ time I will be twice as old as my brother”
How old is each of them now?

2.
Which of the four pieces of rope pictured will form a knot when the two ends are pulled apart, and which will not?

3. A shopkeeper lowers his price on a particular article by 20% for a sale.
At the end of the sale, he raises the price on that article by 20%. Will the article now cost more than, less than or the same as it did before the sale?

4. In the two designs below, combinations of cubes are stacked together.
All the rows are complete unless you can see their end. In other words, you can assume that there are some unseen cubes behind the visible ones.

Based on the visual evidence given, state how many cubes are in each design.

5. Given that when water boils, the temperature readings on the Celsius and Fahrenheit scales are 100°C and 212°F respectively, and that when water freezes, the temperature readings are 0°C and 32°F:
At what temperature are the Celsius and Fahrenheit readings numerically equal?

6.
The drawing above represents two shapes made from gluing coloured hexagonal tiles together. How many different ways can you place the small shape over the larger shape so that it lines up, making a match with the existing colours?
You can spin the small shape around, but you can’t flip it over.

7. A party of people went to a restaurant and each ordered exactly the same meal.
The total bill came to \$44.11. How many were in the party? (Clue: not more than 20)

8. Simple Simon met a pieman going to the fair
Said Simple Simon to the pieman, “How much is your ware”?
Said the pieman to Simple Simon, “It’s seven pence for each of these, and eight pence for each of those”.
“Fair enough”, said Simple Simon, and bought some of these and some of those. The whole lot cost 8 shillings and 1 pence.
How many of these and how many of those did he buy?

9. What is the smallest number that increases by 12 when viewed upside down?

10. A snooker break is made by potting red balls, which are each followed by a ball of a different colour.

A snooker player makes a break of 70, which finishes when he fails to pot the next red. In the break he pots the same number of blue and brown and one more pink than yellow. None of the other colours is potted.
For five points,
a) How many red balls were potted in the break?
b) How many yellow?
c) How many brown?
d) How many blue?
e) How many pink?

SOLUTIONS