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.

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?

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?

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.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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?

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?

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.

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.

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.

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.

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?

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.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

How many models can you find which obey these rules?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Can you find all the different triangles on these peg boards, and find their angles?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

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?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Find out about Magic Squares in this article written for students. Why are they magic?!

How many different triangles can you make on a circular pegboard that has nine pegs?

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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.

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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.

Try out the lottery that is played in a far-away land. What is the chance of winning?

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?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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?

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....?

My coat has three buttons. How many ways can you find to do up all the buttons?