1000 Published Shorts

These problems have been adapted from the 1000 Problems to Enjoy collection.

Point in Between

Age 11 to 14 Short Challenge Level:

Find the point on the line segment AB that is twice as far from B as it is from A.

Mean Square

Age 11 to 14 Short 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?

Age 11 to 14 Short Challenge Level:

What is the sum of these fractions?

Multiple Choice

Age 11 to 14 Short Challenge Level:

How many questions did Sarah answer correctly in this multiple choice exam?

Two Triangles

Age 11 to 14 Short Challenge Level:

Prove that the angle marked $a$ is half the size of the angle marked $b$.

Leg It

Age 11 to 14 Short Challenge Level:

How far from the finishing line should these runners start to make the race 'fair'?

Inner Rectangle

Age 11 to 14 Short Challenge Level:

If the shape on the inside is a rectangle, what can you say about the shape on the outside?

No Rights

Age 11 to 14 Short Challenge Level:

Prove that the angle bisectors of a triangle can never meet at right angles.

Rectangle Split

Age 11 to 14 Short Challenge Level:

Draw another line through the centre of this rectangle to split it into 4 pieces of equal area.

Huge Powers

Age 14 to 16 Short Challenge Level:

Can you put these numbers in order?

Candy Floss

Age 14 to 16 Short Challenge Level:

What length of candy floss can Rita spin from her cylinder of sugar?

A Mean Calculation

Age 14 to 16 Short Challenge Level:

What is the mean of this set of numbers?

Similar Cylinders

Age 14 to 16 Short Challenge Level:

Two similar cylinders are formed from a block of metal. What is the volume of the smaller cylinder?

Loo Roll Emergency

Age 14 to 16 Short Challenge Level:

When the roll of toilet paper is half as wide, what percentage of the paper is left?

Circles on a Triangle

Age 14 to 16 Short Challenge Level:

Find the missing length on this diagram.

Pendants

Age 14 to 16 Short Challenge Level:

What proportion of each of these pendants will be made of gold?

Tunnel Vision

Age 14 to 16 Short Challenge Level:

How wide is this tunnel?

How Many Digits?

Age 14 to 16 Short Challenge Level:

How many digits are there in this product?

Folded Square

Age 14 to 16 Short Challenge Level:

This square piece of paper has been folded and creased. Where does the crease meet the side AD?

Two Equilateral Triangles

Age 14 to 16 Short Challenge Level:

Prove that these two lengths are equal.

Distance to the Corner

Age 14 to 16 Short 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?

Half Area

Age 14 to 16 Short Challenge Level:

The horizontal red line divides this equilateral triangle into two shapes of equal area. How long is the red line?

The Property Market

Age 14 to 16 Short 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?

Snake Eyes

Age 14 to 16 Short Challenge Level:

Can you find the area of the yellow part of this snake's eye?

Domino Match

Age 14 to 16 Short Challenge Level:

If you take two dominoes from a set at random, what is the probability that they 'match'?

Ratio Cut

Age 14 to 16 Short 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?

Semicircle in a Triangle

Age 14 to 16 Short Challenge Level:

A semicircle is drawn inside a right-angled triangle. Find the distance marked on the diagram.

Diamond Ring

Age 14 to 16 Short Challenge Level:

Find the radius of the stone in this ring.

When the Boat Comes In

Age 14 to 16 Short 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?

Backwards Laps

Age 14 to 16 Short 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?

Height of the Tower

Age 14 to 16 Short Challenge Level:

How do these measurements enable you to find the height of this tower?