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.
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 number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
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 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. . . .
Given the products of adjacent cells, can you complete this Sudoku?
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
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?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Use the differences to find the solution to this Sudoku.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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.
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.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
This Sudoku combines all four arithmetic operations.
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?
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 different symmetrical shapes can you make by shading triangles or squares?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
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?