Visualising and representing

problem
Painting possibilities

Age

7 to 11

Challenge level

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes and the small cubes that would fit inside each one.
game

Endless noughts and crosses

Age

7 to 11

Challenge level

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.
game

Counter roundup

Age

7 to 11

Challenge level

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
problem
Tetrahedron faces

Age

7 to 11

Challenge level

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?
problem
Redblue

Age

7 to 11

Challenge level

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?
problem
Shunting puzzle

Age

7 to 11

Challenge level

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
problem
Single track

Age

7 to 11

Challenge level

What is the best way to shunt these carriages so that each train can continue its journey?
problem
Waiting for blast off

Age

7 to 11

Challenge level

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
problem
Counting cards

Age

7 to 11

Challenge level

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
problem
Fitted

Age

7 to 11

Challenge level

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?