A Sudoku with clues given as sums of entries.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
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.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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.
Use the clues to colour each square.
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?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
A challenging activity focusing on finding all possible ways of stacking rods.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
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.
This challenge extends the Plants investigation so now four or more children are involved.
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?
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?
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?
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....?
Find out about Magic Squares in this article written for students. Why are they magic?!
Try out the lottery that is played in a far-away land. What is the chance of winning?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
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?
How many models can you find which obey these rules?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Find out what a "fault-free" rectangle is and try to make some of your own.
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 find all the different triangles on these peg boards, and find their angles?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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.
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 put the numbers 1 to 8 into the circles so that the four calculations are correct?
How many different rhythms can you make by putting two drums on the wheel?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Can you find all the different ways of lining up these Cuisenaire rods?
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.
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.