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?
A few extra challenges set by some young NRICH members.
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?
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?
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 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.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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. . . .
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?
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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.
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 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. . . .
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.
Given the products of adjacent cells, can you complete this Sudoku?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
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?
Four friends must cross a bridge. How can they all cross it in just
Find the values of the nine letters in the sum: FOOT + BALL = GAME
This challenge extends the Plants investigation so now four or more children are involved.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
A challenging activity focusing on finding all possible ways of stacking rods.
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
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...
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.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Four small numbers give the clue to the contents of the four
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
Use the differences to find the solution to this Sudoku.
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?
A pair of Sudoku puzzles that together lead to a complete solution.
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
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?
A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.