Working systematically

problem
Plenty of pens

Age

7 to 11

Challenge level

Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?
problem
Money bags

Age

5 to 11

Challenge level

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
problem
Fractions in a box

Age

7 to 11

Challenge level

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
problem
Routes 1 and 5

Age

5 to 7

Challenge level

Find your way through the grid starting at 2 and following these operations. What number do you end on?
problem
A shapely network

Age

7 to 11

Challenge level

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.
problem
Home time

Age

7 to 11

Challenge level

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.
problem
Colour in the square

Age

7 to 16

Challenge level

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
problem
Four colours

Age

5 to 11

Challenge level

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
problem
A bit of a dicey problem

Age

7 to 11

Challenge level

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
problem
A-magical number maze

Age

7 to 11

Challenge level

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!