How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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!
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
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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 number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
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.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
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.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
How many different symmetrical shapes can you make by shading triangles or squares?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?