In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This article for primary teachers suggests ways in which to help children become better at working systematically.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
A Sudoku with clues given as sums of entries.
This challenge extends the Plants investigation so now four or more children are involved.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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.
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.
A challenging activity focusing on finding all possible ways of stacking rods.
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Use the clues to colour each square.
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
How many different triangles can you make on a circular pegboard that has nine pegs?
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.
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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....?
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
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?
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?
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 triangle.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you cover the camel with these pieces?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
What happens when you try and fit the triomino pieces into these
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?
Can you find all the different triangles on these peg boards, and
find their angles?
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?
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
How many different rhythms can you make by putting two drums on the
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Find out what a "fault-free" rectangle is and try to make some of
Can you find all the different ways of lining up these Cuisenaire
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?