A challenging activity focusing on finding all possible ways of stacking rods.
How many different symmetrical shapes can you make by shading triangles or squares?
This challenge extends the Plants investigation so now four or more children are involved.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
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.
Use the clues about the symmetrical properties of these letters to
place them on the grid.
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.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
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 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?
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
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.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
This activity investigates how you might make squares and pentominoes from Polydron.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Can you find all the different triangles on these peg boards, and
find their angles?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Find out what a "fault-free" rectangle is and try to make some of
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
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 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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Can you find all the different ways of lining up these Cuisenaire
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?