Visualising and representing

problem
Spotting the loophole

Age

14 to 16

Challenge level

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?
problem
Painted faces

Age

7 to 11

Challenge level

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
problem
Flip

Age

7 to 11

Challenge level

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?
problem
Picture a pyramid

Age

7 to 11

Challenge level

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
problem
Cube drilling

Age

7 to 11

Challenge level

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
problem
Ace, two, three...

Age

11 to 14

Challenge level

Can you picture how to order the cards to reproduce Charlie's card trick for yourself?
problem
Dicey directions

Age

14 to 16

Challenge level

An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?
problem
Night watchmen

Age

11 to 14

Challenge level

Grannie's watch gains 30 minutes every hour, whilst Grandpa's watch loses 30 minutes every hour. What is the correct time when their watches next agree?
problem
Twelve cubed

Age

14 to 16

Challenge level

A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?
problem
Cheese cutting

Age

16 to 18

Challenge level

In this problem we see how many pieces we can cut a cube of cheese into using a limited number of slices. How many pieces will you be able to make?