A challenging activity focusing on finding all possible ways of stacking rods.
This challenge extends the Plants investigation so now four or more children are involved.
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.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
How many different symmetrical shapes can you make by shading triangles or squares?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
A few extra challenges set by some young NRICH members.
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. . . .
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Four friends must cross a bridge. How can they all cross it in just
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
This activity investigates how you might make squares and pentominoes from Polydron.
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you find all the different ways of lining up these Cuisenaire
Can you find all the different triangles on these peg boards, and
find their angles?
Find out what a "fault-free" rectangle is and try to make some of
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.
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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?"
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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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.
Given the products of adjacent cells, can you complete this Sudoku?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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...
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?
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 package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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....?
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.