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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
A few extra challenges set by some young NRICH members.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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?
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. . . .
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.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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.
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.
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 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. . . .
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.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
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.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
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?
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?"
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
This challenge extends the Plants investigation so now four or more children are involved.
Can you use the information to find out which cards I have used?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.