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?"
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?
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. . . .
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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.
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 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?
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?
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.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Given the products of adjacent cells, can you complete this Sudoku?
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. . . .
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
A few extra challenges set by some young NRICH members.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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...
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 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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
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.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Four small numbers give the clue to the contents of the four
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
This challenge extends the Plants investigation so now four or more children are involved.
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.
A challenging activity focusing on finding all possible ways of stacking rods.
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
A pair of Sudoku puzzles that together lead to a complete solution.