Exploring and noticing
problem
Favourite
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
problem
Favourite
Back fitter
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
problem
Favourite
Partly painted cube
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
problem
Favourite
Ip dip
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
problem
Favourite
Pebbles
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
problem
Favourite
Round and round the circle
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
problem
Favourite
Differences
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
problem
Favourite
Prison cells
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
problem
Favourite
Numerically equal
Can you draw a square in which the perimeter is numerically equal to the area?