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 in them?
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.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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 Sudoku with clues given as sums of entries.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you cover the camel with these pieces?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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 do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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?
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.
What happens when you try and fit the triomino pieces into these
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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.
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?
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?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
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?
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.
Can you find all the different triangles on these peg boards, and
find their angles?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
This challenge extends the Plants investigation so now four or more children are involved.
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.
What could the half time scores have been in these Olympic hockey matches?
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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 tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A challenging activity focusing on finding all possible ways of stacking rods.
In this matching game, you have to decide how long different events take.
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.
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
Try this matching game which will help you recognise different ways of saying the same time interval.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?