Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
A Sudoku with clues given as sums of entries.
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.
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?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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 this article, the NRICH team describe the process of selecting solutions for publication on the site.
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 your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Use the clues to colour each square.
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.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
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....?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
How many models can you find which obey these rules?
A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?
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?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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 interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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?
Can you find all the different triangles on these peg boards, and find their angles?
Can you find all the different ways of lining up these Cuisenaire rods?
What happens when you try and fit the triomino pieces into these two grids?
Find out what a "fault-free" rectangle is and try to make some of your own.
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.
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.
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?
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.
How many different rhythms can you make by putting two drums on the wheel?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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.
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.