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?
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.
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?
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?
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?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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?
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.
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?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
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?
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.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you coach your rowing eight to win?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
A Sudoku with clues as ratios or fractions.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
A Sudoku with clues as ratios.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Given the products of diagonally opposite cells - can you complete this Sudoku?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
A few extra challenges set by some young NRICH members.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
A Sudoku with a twist.
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
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?
Two sudokus in one. Challenge yourself to make the necessary
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.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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?
A Sudoku that uses transformations as supporting clues.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Given the products of adjacent cells, can you complete this Sudoku?
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.
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
This challenge extends the Plants investigation so now four or more children are involved.