## May 2013 Logic & Maths Puzzles

1. I am thinking of a whole number between 1 and 20, inclusive.
• If my number is less than 10, then it is even.
• If my number is not divisible by 3, then it is prime.
• If my number is not a factor of 60, then it is a factor of 102.
• If my number, divided by 7, leaves a remainder greater than 4, then my number is greater than 14.
• If one less than my number is a square number, then the reciprocal of my number is less than 3/7.
• If one more than my number is a square number, then my number is not divisible by 5.
What is my number?

2. I am thinking of another whole number between 1 and 20, inclusive.
• Either my number is greater than the hypotenuse of a right triangle with sides of 5 and 12, or it is less than the diameter of a circle with an area of 48.
• My number is less than the longest possible side of a triangle with sides of 7 and 11, and greater than the shortest possible side of the same triangle.
• My number is either odd or a multiple of five, but not both.
• My number is the smaller of the two numbers that fit all of the above requirements.
What is my number?

3. You have a cylindrical container just big enough to hold three tennis balls. Now you want to make a label for the container, and you have to decide whether to wrap the label around the cylinder or up the side.

Which direction is longer?
Assume that the container wall is so thin as to be negligible.

4. What is the next number in this sequence?
30, 28, 25, 21, 16 _

5. The diagram represents a green metal disc of 100 centimetres diameter.
It has had five 20 centimetre diameter holes bored through it.

Before boring, the disc weighed 10 kg. What does it weigh after boring?

6. Yesterday, I had 84 photos in album a, and 20 photos in album b.
Today, I put x photos in each album. Now, the number of photos in album a is 3 times the number of photos of album b.
Find x.

7. Seven cards have been dealt face up.

Identify the first, third and fifth cards to be dealt.

8. Look at the set of three squares at the top.

They have a certain feature which is shared by only one of the four groups of three squares below.

a. What is it?

b. Which group shares this feature:
a, b, c or d?

9. This is a cryptogram, in which a simple (and relevant) message is coded using a simple letter-for-letter substitution. Can you solve it?

10. Tom asked his Granny how old she was. Rather than giving him a straight answer, she replied:
“I have 6 children, and there are 4 years between each one and the next. I had my first child (your Uncle Peter) when I was 19. Now the youngest one (Your Auntie Jane) is 19 herself. That’s all I’m telling you!”
How old is Tom’s Granny?

SOLUTIONS