Challenge Level

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.

Challenge Level

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?

Challenge Level

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?

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.

Challenge Level

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

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.

Challenge Level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Challenge Level

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?

Challenge Level

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

Challenge Level

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Challenge Level

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

Challenge Level

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Challenge Level

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

Challenge Level

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Challenge Level

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?

Challenge Level

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Challenge Level

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Challenge Level

Given the products of diagonally opposite cells - can you complete this Sudoku?

Challenge Level

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

Challenge Level

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

Challenge Level

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Challenge Level

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

Challenge Level

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

Challenge Level

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

Challenge Level

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?

Challenge Level

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.

Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Challenge Level

In this game you are challenged to gain more columns of lily pads than your opponent.

Challenge Level

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

Challenge Level

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

Challenge Level

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

Challenge Level

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

Challenge Level

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?

Challenge Level

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.

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

Challenge Level

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

Challenge Level

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

Challenge Level

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Challenge Level

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.

Challenge Level

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

Challenge Level

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