Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

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 arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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.

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

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?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

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.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Four small numbers give the clue to the contents of the four surrounding cells.

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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.

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

A Sudoku that uses transformations as supporting clues.

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Given the products of adjacent cells, can you complete this Sudoku?

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

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

A pair of Sudoku puzzles that together lead to a complete solution.

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

Use the differences to find the solution to this Sudoku.

Two sudokus in one. Challenge yourself to make the necessary connections.

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?

How many different symmetrical shapes can you make by shading triangles or squares?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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.

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 use your powers of logic and deduction to work out the missing information in these sporty situations?

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.

Use the clues about the shaded areas to help solve this sudoku

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

This Sudoku, based on differences. Using the one clue number can you find the solution?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?