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.
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?
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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.
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.
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
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 the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
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.
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
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.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you find all the different triangles on these peg boards, and find their angles?
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.
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?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
My coat has three buttons. How many ways can you find to do up all the buttons?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?