## December 2013 Logic & Maths Puzzles

1. The diagram on the right represents three identical yellow square tiles meeting at a corner, with three identical grey triangular tiles assembled as shown. State the size of angle a in degrees

2. 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 74, which finishes when he fails to pot the next red. In the break he pots more blacks than browns and more blues than pinks. None of the other colours is potted.
a) How many red balls were potted in the break?
b) How many brown?
c) How many blue?
d) How many pink?
e) How many black?

3. A snooker player makes a break of 69, which finishes when he fails to pot the next red. In the break he pots less black than blue and more brown than yellow. None of the other colours is potted.
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 black?

4. A gambler doubles his money then gives away \$10. He then triples his money and gives away \$20, leaving him with four times the amount of money that he started with. How much money did he start with?

5. The sum of the squares of two consecutive numbers is 1861. What are the two numbers?

6. 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.

7.
In a fitness exercise, a runner must collect five “witches hats” one at a time, returning to the start with the closest one before setting off to collect the next one, and so on, before finally running the distance from start to finish. If all intervals are 8m as shown,
What is the total distance the runner must run?

8. A marksman averaged 22 points for his first 10 rounds. After another 20 rounds his average had increased to 34 points. What was his average for the last 20 rounds?

9. In a certain fruit shop on a certain day, Shopper A purchased 3 apples, 6 bananas and a cantaloupe, while Shopper B purchased 4 apples, 3 bananas and 2 cantaloupes. Shoppers A and B both paid \$5.10 each.
Shopper C bought an apple, while Shopper D bought a banana. Shopper D paid 20 cents more than Shopper C.
What was the price for each apple, each banana and each canteloupe?

10. In a supermarket, the aisles are numbered 1 to 6 from the entrance.
Washing powder is in the aisle next to the aisle containing the bottles of tomato sauce, and is not in the first aisle you see when entering the supermarket.
You see the meat aisle sometime before you encounter the bread aisle.
Tins of jam are two aisles before the bottles of tomato sauce and the meat is four aisles after the fresh fruit.
If all six aisles have been mentioned:
a. What is in the first aisle (aisle 1)?
b. What is in the last aisle (aisle 6)?
c. In which aisle are the bottles of tomato sauce?

SOLUTIONS