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

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?

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?

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

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?

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.

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.

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 NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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.

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

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?

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

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

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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?

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

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 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?

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

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

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

A challenging activity focusing on finding all possible ways of stacking rods.

You need to find the values of the stars before you can apply normal Sudoku rules.

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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.

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.

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?

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?

This challenge extends the Plants investigation so now four or more children are involved.

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

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

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

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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

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

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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

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

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?