Visualising and representing

problem
Funny factorisation

Age

11 to 16

Challenge level

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
problem
Five circuits, seven spins

Age

16 to 18

Challenge level

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.
problem
Middle man

Age

16 to 18

Challenge level

Mark a point P inside a closed curve. Is it always possible to find two points that lie on the curve, such that P is the mid point of the line joining these two points?
problem
Neighbours

Age

7 to 11

Challenge level

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
problem
Soma - so good

Age

11 to 14

Challenge level

Can you mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?
problem
How many dice?

Age

11 to 14

Challenge level

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find there are 2 and only 2 different standard dice. Can you prove this ?
problem
Rolling triangle

Age

11 to 14

Challenge level

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.
problem
Sitting pretty

Age

14 to 16

Challenge level

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
problem
Weighty problem

Age

11 to 14

Challenge level

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it is facing the other way round.
problem
Plus minus

Age

14 to 16

Challenge level

Can you explain the surprising results Jo found when she calculated the difference between square numbers?