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.
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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.
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.
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.
Find all the numbers that can be made by adding the dots on two dice.
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 work out how to balance this equaliser? You can put more than one weight on a hook.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
How many models can you find which obey these rules?
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?
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?
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
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.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
What happens when you try and fit the triomino pieces into these two grids?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Find out about Magic Squares in this article written for students. Why are they magic?!
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....?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
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 find all the different ways of lining up these Cuisenaire rods?
Can you find all the different triangles on these peg boards, and find their angles?
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
How many different triangles can you make on a circular pegboard that has nine pegs?
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.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?