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.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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.
How many different symmetrical shapes can you make by shading triangles or squares?
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.
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?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
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?
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
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?
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?
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.
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.
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
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?
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?
Solve the equations to identify the clue numbers in this Sudoku problem.
This Sudoku requires you to do some working backwards before working forwards.
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?
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
A Sudoku with a twist.
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?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
A Sudoku with a twist.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
How long does it take to brush your teeth? Can you find the matching length of time?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
A Sudoku with clues as ratios or fractions.
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
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 challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
The pages of my calendar have got mixed up. Can you sort them out?