Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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 irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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.
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
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
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?
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!
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
Can you use this information to work out Charlie's house number?
Can you replace the letters with numbers? Is there only one solution in each case?
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?
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?
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
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!
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.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
A few extra challenges set by some young NRICH members.
Given the products of adjacent cells, can you complete this Sudoku?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
This challenge extends the Plants investigation so now four or more children are involved.
How many different symmetrical shapes can you make by shading triangles or squares?
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
A challenging activity focusing on finding all possible ways of stacking rods.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of