## July 2017 Logic & Maths Problems

1. How many edges does a tetrahedron have?

2. Twelve contestants are narrowed down to three in a KNOCKOUT competition.
The winner is then decided by best performance in a ROUND ROBIN.
How many matches are played in total?

3. Three quarters of the time already passed on a 99 year lease is equal to three fifths of the time left to serve on the lease. How many years have passed on the lease?

4. Mr. Johnson and Mr. Smith decided to start a business together. It was to be called “Johnson and Smith.” Unfortunately when painting the shop window, the sign-writer made a mistake and the sign read as follows:

Johnson was very cross and proceeded to tell off the sign-writer. In telling him off, how can he use the word ‘and’ five times in a row, and still make a proper sentence?

5. How many times faster does the second hand of a clock rotate than the hour hand?

6. You are on your way to visit your Grandma, who lives at the end of the valley. It’s her birthday, and you want to give her the cakes you’ve made.

Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is a troll under every bridge!

Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.

How many cakes do you have to leave home with to make sure that you arrive at Grandma’s with exactly 2 cakes?

7. In a jar there are 11 animals of three different species.
There is at least one ant, at least one spider and at least one centipede.
All in all they share 122 legs; none is missing any of its legs.
Given this information, what is the greatest number of legs possible for any centipede in the jar?
(NOTE: Most centipedes do not have 100 legs. The number of legs varies from species to species. A fully equipped adult centipede can have between 30 and 354 legs.)

8. At a certain fruit-and-veggie shop, one bunch each of carrots, spring onions and parsnips have a total cost of \$10.97.
Two bunches of carrots and a bunch of spring onions cost \$7.97,
and a shopper who buys one bunch of carrots, one bunch of spring onions and two bunches of parsnips will pay one cent more than a shopper who buys three bunches of carrots and one bunch each of spring onions and parsnips.
What is the cost per bunch of carrots, spring onions and parsnips in that order?

9. A, B and C are integers (whole numbers) less than or equal to 9. In other words,
A is any whole number from 1 to 9 inclusive
B is any whole number from 1 to 9 inclusive
C is any whole number from 1 to 9 inclusive

AAA  +  BBB   +   CCC  =   CBBC

What is the value of A, B & C respectively?

10. What is the lowest prime number above 1000?

SOLUTIONS