Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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. . . .
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?
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?
Four friends must cross a bridge. How can they all cross it in just
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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?
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
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.
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. . . .
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 Sudoku, based on differences. Using the one clue number can you find the solution?
In this matching game, you have to decide how long different events take.
This challenge extends the Plants investigation so now four or more children are involved.
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
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.
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
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?