Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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.
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 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?
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!
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?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Find out what a "fault-free" rectangle is and try to make some of
Investigate the different ways you could split up these rooms so
that you have double the number.
How many different triangles can you make on a circular pegboard that has nine pegs?
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.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
How many different rhythms can you make by putting two drums on the
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Sitting around a table are three girls and three boys. Use the
clues to work out were each person is sitting.
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
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
My coat has three buttons. How many ways can you find to do up all
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
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.
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
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
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?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
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?
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.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?