Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
Use the differences to find the solution to this Sudoku.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Four small numbers give the clue to the contents of the four
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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.
Can you use the information to find out which cards I have used?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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 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?
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.
Two sudokus in one. Challenge yourself to make the necessary
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
A Sudoku with a twist.
The puzzle can be solved with the help of small clue-numbers which
are either placed on the border lines between selected pairs of
neighbouring squares of the grid or placed after slash marks on. . . .
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
A Sudoku with clues as ratios.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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.
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
A Sudoku with clues as ratios or fractions.
This challenge extends the Plants investigation so now four or more children are involved.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
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 Sudoku combines all four arithmetic operations.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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.
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
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?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
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?
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 could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?