Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
The idea of this game is to add or subtract the two numbers on the
dice and cover the result on the grid, trying to get a line of
three. Are there some numbers that are good to aim for?
Find out what a "fault-free" rectangle is and try to make some of
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Find all the numbers that can be made by adding the dots on two dice.
Can you find all the different triangles on these peg boards, and
find their angles?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
A Sudoku with clues given as sums of entries.
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?
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?
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.
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
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?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
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.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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
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 interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many trains can you make which are the same length as Matt's,
using rods that are identical?
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
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?
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Can you find all the different ways of lining up these Cuisenaire
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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 tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
What is the least number of moves you can take to rearrange the
bears so that no bear is next to a bear of the same colour?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.