This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Can you substitute numbers for the letters in these sums?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
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?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
How many triangles can you make on the 3 by 3 pegboard?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
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?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
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?
Ben has five coins in his pocket. How much money might he have?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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?
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
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
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 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Investigate the different ways you could split up these rooms so
that you have double the number.
An activity making various patterns with 2 x 1 rectangular tiles.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
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!
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
How many models can you find which obey these rules?
Can you use the information to find out which cards I have used?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.