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.
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?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
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?
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.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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.
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.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
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?
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 six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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.
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 work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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 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.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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....?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
My coat has three buttons. How many ways can you find to do up all
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.
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
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 models can you find which obey these rules?
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
How many different triangles can you make on a circular pegboard that has nine pegs?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
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?
Can you fill in the empty boxes in the grid with the right shape
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you find all the different ways of lining up these Cuisenaire
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
Find all the numbers that can be made by adding the dots on two dice.