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?
A Sudoku with clues given as sums of entries.
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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 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.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
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?
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.
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.
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?
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.
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?
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
My coat has three buttons. How many ways can you find to do up all
Can you rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?
How many models can you find which obey these rules?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Find all the numbers that can be made by adding the dots on two dice.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Can you find all the different triangles on these peg boards, and
find their angles?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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.
What happens when you try and fit the triomino pieces into these
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
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....?
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?