Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 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?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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?
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
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.?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?
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?
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 eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
Can you find out in which order the children are standing in this line?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
Can you use this information to work out Charlie's house number?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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?
When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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.
How many trapeziums, of various sizes, are hidden in this picture?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
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 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?
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?