These problems have been adapted from the 1000 Problems to Enjoy [http://1000problems.org/] collection.
problem
Two Triangles
Age
11 to 14
Challenge level
Prove that the angle marked $a$ is half the size of the angle marked $b$.
problem
Point in between
Age
11 to 14
Challenge level
Find the point on the line segment AB that is twice as far from B as it is from A.
problem
Mean Square
Age
11 to 14
Challenge level
Can you fill this square so that the number in the middle of each line is the mean of the two numbers on either side of it?
problem
Multiple choice
Age
11 to 14
Challenge level
How many questions did Sarah answer correctly in this multiple choice exam?
problem
Leg It
Age
11 to 14
Challenge level
How far from the finishing line should these runners start to make the race 'fair'?
problem
rectangle split
Age
11 to 14
Challenge level
Draw another line through the centre of this rectangle to split it into 4 pieces of equal area.
problem
inner rectangle
Age
11 to 14
Challenge level
If the shape on the inside is a rectangle, what can you say about the shape on the outside?
problem
No rights
Age
11 to 14
Challenge level
Prove that the angle bisectors of a triangle can never meet at right angles.
problem
Pendants
Age
14 to 16
Challenge level
What proportion of each of these pendants will be made of gold?
problem
Loo roll emergency
Age
14 to 16
Challenge level
When the roll of toilet paper is half as wide, what percentage of the paper is left?
problem
Candy floss
Age
14 to 16
Challenge level
What length of candy floss can Rita spin from her cylinder of sugar?
problem
Similar Cylinders
Age
14 to 16
Challenge level
Two similar cylinders are formed from a block of metal. What is the volume of the smaller cylinder?
problem
When the boat comes in
Age
14 to 16
Challenge level
When you pull a boat in using a rope, does the boat move more quickly, more slowly, or at the same speed as you?
problem
Two equilateral triangles
Age
14 to 16
Challenge level
Prove that these two lengths are equal.
problem
Semicircle in a Triangle
Age
14 to 16
Challenge level
A semicircle is drawn inside a right-angled triangle. Find the distance marked on the diagram.
problem
Height of the Tower
Age
14 to 16
Challenge level
How do these measurements enable you to find the height of this tower?
problem
Folded Square
Age
14 to 16
Challenge level
This square piece of paper has been folded and creased. Where does the crease meet the side AD?
problem
Half Area
Age
14 to 16
Challenge level
The horizontal red line divides this equilateral triangle into two shapes of equal area. How long is the red line?
problem
Snake eyes
Age
14 to 16
Challenge level
Can you find the area of the yellow part of this snake's eye?
problem
The property market
Age
14 to 16
Challenge level
A property developer sells two houses, and makes a 20% loss on one and a 20% profit on the other. Overall, did he make a profit or a loss?
problem
Domino Match
Age
14 to 16
Challenge level
If you take two dominoes from a set at random, what is the probability that they 'match'?
problem
Backwards laps
Age
14 to 16
Challenge level
If two friends run in opposite directions around a track, and they pass each other every 24 seconds, how long do they take to complete a lap?
problem
Distance to the corner
Age
14 to 16
Challenge level
Can you find the distance from the well to the fourth corner, given the distance from the well to the first three corners?
problem
ratio cut
Age
14 to 16
Challenge level
Cutting a rectangle from a corner to a point on the opposite side splits its area in the ratio 1:2. What is the ratio of a:b?