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 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?"
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 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. . . .
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
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.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Given the products of adjacent cells, can you complete this Sudoku?
Can you find all the different ways of lining up these Cuisenaire
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Investigate the different ways you could split up these rooms so
that you have double the number.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
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?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
In how many ways can you stack these rods, following the rules?
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
In this matching game, you have to decide how long different events take.
This dice train has been made using specific rules. How many different trains can you make?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
How many triangles can you make on the 3 by 3 pegboard?
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.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.