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.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Four small numbers give the clue to the contents of the four
This Sudoku, based on differences. Using the one clue number can you find the solution?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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.
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
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?
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.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
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?
Two sudokus in one. Challenge yourself to make the necessary
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.
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?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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?
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.
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.
A Sudoku with a twist.
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?
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?
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 Sudoku combines all four arithmetic operations.
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.
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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.
A Sudoku that uses transformations as supporting clues.
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
A Sudoku with clues as ratios.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A Sudoku with clues as ratios or fractions.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
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?
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?
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.
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
You need to find the values of the stars before you can apply normal Sudoku rules.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this