Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
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?
Find out what a "fault-free" rectangle is and try to make some of
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
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?
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!
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
How many different triangles can you make on a circular pegboard that has nine pegs?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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
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?
The Zargoes use almost the same alphabet as English. What does this
birthday message say?
How many trapeziums, of various sizes, are hidden in this picture?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
What is the smallest number of jumps needed before the white
rabbits and the grey rabbits can continue along their path?
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 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?
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 triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
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 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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?
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?
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.