## March 2014 Logic & Maths Puzzles

1. A player scores 83 with three darts, hitting a treble, a double and a single (no bulls).

Given that the three numbers that he hits add up to 36 and that the difference between the largest and smallest numbers is 16, how is his score made up?
Please write your answer in the form Treble = _ , Double = _, Single = _.

2. In a certain game, the object is to collect different coloured balls.
Each colour represents a different whole number value.
The picture above represents the situation at the end of a game.
What was player D’s score?

3. In each case, write the next number in the sequence (i.e. the number represented by “x”.)
a. 0, 1, 3, 6, 10, 15, x
b. 1, 1, 2, 3, 5, 8, 13, 21, x
c. 1, 2, 4, 8, 16, 32, 64, 128, x
d. 1, 8, 27, 64, 125, 216, x
e. -1, 0, 3, 8, 15, 24, 35, 48, 63, 80, x
f. 1, 4, 27, 256, x

4. What is the sum of:
a. The number of Days in a Week + The number of Months in a Year + The number of Hours in a Day?
b. The number of Commandments + The number of Deadly Sins + the number of calling birds in “The Twelve Days of Christmas?
c. number of Ways to Leave Your Lover + “the loneliest number” + The number of Trombones that lead the big parade?
d. The number of Snow White’s dwarves + the number of Little Pigs + the number of Blind Mice + the number of people it takes to tango?
e. A pair + a dozen + a score + a century + a gross?

5.
How many triangles are there in this diagram?

6.
In each vertical column the letters add up to 10.
What letter belongs in the empty box?

7. A farmer keeps only four types of animals; pigs, cows, sheep and horses.
He has a total of 560 animals.
IF he had 10 sheep fewer, he would have twice as many sheep as he has cows.
IF he had 10 cows fewer, he would have 3 cows to every pig.
He has two and a half pigs to every horse.
how many of each animal does he have?

8.
At 3pm one day, a flagpole and a measuring pole cast shadows as shown. What is the height of the flagpole?

9. How many male and how many female rabbits are there in a family of rabbits if each male rabbit has one fewer female relative than he has male relatives, and each female rabbit has two males fewer than twice the number of female relatives she has?

10.
Furius Maximus is not a happy centurion.
One cohort of 12 troops performed so badly in the last battle that he’s decided to make an example of them.

He forms them in a circle and has them number off as shown.

He then commands the execution of every fifth man as follows; number 1 marches clockwise (bypassing 2,3 and 4) until he reaches number 5, whom he kills before returning to position. Number 6, as next man, kills number 10.

But Furius is still not satisfied. He orders soldier 11 to kill soldier 3 and so on. As each
survivor gets his turn as executioner, he continues the pattern, counting off the other survivors in clockwise fashion while ignoring the dead.
a. How many of the cohort will be left standing (assuming no soldier is required to execute himself, or move around the circle more than once)?
b. Give their numbers.

SOLUTIONS