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.
A Sudoku with clues given as sums of entries.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
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.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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.
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.
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 what a "fault-free" rectangle is and try to make some of your own.
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
An investigation that gives you the opportunity to make and justify predictions.
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
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.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Investigate the different ways you could split up these rooms so that you have double the number.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
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?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
Try out the lottery that is played in a far-away land. What is the chance of winning?
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
My coat has three buttons. How many ways can you find to do up all the buttons?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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.
Can you find all the different triangles on these peg boards, and find their angles?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
This challenge extends the Plants investigation so now four or more children are involved.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
What could the half time scores have been in these Olympic hockey matches?
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.