## July 2016 Logic & Maths Problems

1. I have a jar of lollies, 252 yellow, 227 blue, 331 green and 90 red. What chance do I have of picking a red one with my eyes shut?

2. What is 2 divided by a quarter?

3.
In a certain army, you only salute officers of equal or higher rank to yourself. Two Generals, two Colonels, two majors, two captains and two lieutenants enter a room.
How many salutes are there?

4. Alice is twice Bill’s age and one year older than Charlie. Charlie was twice Bill’s age a year ago. How old are Alice, Charlie and Bill?

5. Tommy wants to save \$30 to buy his mum a gift.
On day 1 he puts 10 cents in his piggy bank, on day 2 a further 20 cents, on day 3 a further 30 cents and so on. Following this pattern, on which day will he reach his savings goal?

6. Bill has \$10 more than Joe. Fred has half as much money as Joe and \$14 less than Bill. How much money in total do Bill, Fred and Joe have between them?

7. You have teleported down to a hitherto unvisited planet, upon which you discover the following:
1. No two inhabitants have the same number of hairs on their head.
2. No inhabitant has exactly 518 hairs.
3. There are more inhabitants in town than hairs on any individual inhabitant’s head.
4. None of the inhabitants is totally bald.
What is the highest possible number of inhabitants?

8. If a man travels at speed of 20km/hr, he reaches the office 20 minutes late. If he travels at 30 km/hr, he reaches the office 15 minutes early. If he travels at a speed of 25 km/hr, does he arrive:
exactly on time?
5 minutes early?
2 minutes early?
1 minute early?
1 minute late?
2 minutes late?
5 minutes late?

9. A set of football matches is to be organized in a round robin fashion; i.e every participating teams plays a match against every other team once. If 45 matches are played, how many teams participated?

10. A solo dice game is played where, on each turn, a normal pair of dice is rolled. The score is calculated by taking the product, rather than the sum, of the two numbers shown on the dice.
In a particular game, the score for the second roll is five more than the score for the first; the score for the third roll is six less than that of the second; the score for the fourth roll is eleven more than that of the third; and the score for the fifth roll is eight less than that of the fourth. What was the score for each of these five throws?

a. What was the score for the first throw?
b. What was the score for the second throw?
c. What was the score for the third throw?
d. What was the score for the fourth throw?
e. What was the score for the fifth throw?

(Hint: for one throw, the lowest possible score is 1 X 1 =1; the highest possible score is 6 X 6 = 36; what other scores are possible?)

SOLUTIONS