Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
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!
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
Choose a symbol to put into the number sentence.
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 six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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.
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
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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!
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
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?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book 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.
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Can you hang weights in the right place to make the equaliser
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
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?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Find all the numbers that can be made by adding the dots on two dice.