Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?
Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
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?
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
How many models can you find which obey these rules?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
What is the best way to shunt these carriages so that each train can continue its journey?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
What could the half time scores have been in these Olympic hockey matches?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
This activity investigates how you might make squares and pentominoes from Polydron.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?