Working systematically

problem
Put out

Age

16 to 18

Challenge level

After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?
problem
LOGO challenge - the logic of LOGO

Age

11 to 16

Challenge level

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
problem
Counters

Age

7 to 11

Challenge level

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
problem
A square deal

Age

7 to 11

Challenge level

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
problem
Symmetry challenge

Age

7 to 11

Challenge level

How many symmetric designs can you make on this grid? Can you find them all?
problem
Shady symmetry

Age

11 to 14

Challenge level

How many different symmetrical shapes can you make by shading triangles or squares?
problem
Pick's theorem

Age

14 to 16

Challenge level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
problem
Cinema problem

Age

11 to 14

Challenge level

A cinema has 100 seats. How can ticket sales make £100 for these different combinations of ticket prices?
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?
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?