Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 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?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
A Sudoku with clues given as sums of entries.
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?
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
Find out what a "fault-free" rectangle is and try to make some of your own.
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.
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?
Can you find all the different triangles on these peg boards, and find their angles?
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.
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?
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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?
A Sudoku that uses transformations as supporting clues.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Can you find all the different ways of lining up these Cuisenaire rods?
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .
George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?
Two sudokus in one. Challenge yourself to make the necessary connections.
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.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
A Sudoku with a twist.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red 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.
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?
Can you coach your rowing eight to win?
A few extra challenges set by some young NRICH members.
A Sudoku with clues as ratios.
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
Use the differences to find the solution to this Sudoku.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?