A challenging activity focusing on finding all possible ways of stacking rods.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How many different symmetrical shapes can you make by shading triangles or squares?
Use the clues about the symmetrical properties of these letters to
place them on the grid.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
Can you use the information to find out which cards I have used?
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 man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
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.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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. . . .
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?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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?"
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
A few extra challenges set by some young NRICH members.
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?
Four friends must cross a bridge. How can they all cross it in just
Given the products of adjacent cells, can you complete this Sudoku?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
Four small numbers give the clue to the contents of the four
Can you draw a square in which the perimeter is numerically equal
to the area?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
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. . . .
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
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.
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?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
How many necklaces can you make that fit the rule? How do you know you've got them all?
Follow the clues to find the mystery number.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
In how many ways can you stack these rods, following the rules?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Use the differences to find the solution to this Sudoku.
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?