August 2012 Logic & Maths Puzzles
1. 
2. 
In the diagram, the blue shapes are equilateral triangles, and the red shapes are similar triangles. What is the size of angle x?
3. A shopper makes three successive purchases at different stores. Each time, she spends two thirds of what she has. After her third and last purchase, she still has a dollar for the bus home. How much money did she start with?
4. For a number to be a perfect number, it must be the sum of all its factors. For example, 6 is the smallest perfect number. Its factors are 1,2 and 3.
1 + 2 + 3 = 1 X 2 X 3
What is the NEXT perfect number? (HINT: it’s between 10 and 40)
5.
The seven colours of the tiles in the diagram are: blue, red, green, brown, purple, yellow and grey. Each colour has been given a different value from 1 to 7. The number at the end of each row or column is the sum of the values of each coloured tile in that row or column. What is the numerical value of each colour?
6. 
The circle in this diagram has a centre at O and a diameter of 20 cm. If the green lines intersect each other at right angles, what is the length of line AB?
7. Alice, Brenda & Cathy share a birthday today. Alice’s age is 80% of Brenda’s and Brenda’s age is 5/6 that of Cathy’s. Six years ago, Brenda was the same age as Alice is now. How old are Alice, Brenda and Cathy?
8. The “Map Problem” is interesting. The question is:
What is the minimum number of colours required to draw a map so that no two adjacent regions have the same colour?
Everyone agrees on the answer; no-one has been able to mathematically prove it! What is the accepted answer? Here’s a map of the continental USA to practice on. 
9. 
(click to enlarge)
The upper diagram shows a 5 m X 3 m rectangle sitting on a flat plane (eg a box seen side-on sitting on the ground). It is shifted to the right by rolling or rotating it clockwise through 360 degrees so that it comes to rest on each of its four sides in turn.
The other four diagrams, drawn to the same scale represent four possible paths taken by point A as the rectangle rotates through one complete turn. Which one is correct?
10. 
How many triangles are there in total in this figure?