How many trains can you make which are the same length as Matt's,
using rods that are identical?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Can you find all the different ways of lining up these Cuisenaire
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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.
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
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?
Find out what a "fault-free" rectangle is and try to make some of
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
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?
What is the smallest number of jumps needed before the white
rabbits and the grey rabbits can continue along their path?
How many trapeziums, of various sizes, are hidden in this picture?
The Zargoes use almost the same alphabet as English. What does this
birthday message say?
Place the numbers 1 to 10 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
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.?
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?
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?
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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 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?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
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.
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?
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?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the