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 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?
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?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
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.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
How many different symmetrical shapes can you make by shading triangles or squares?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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?
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?
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?
Use the differences to find the solution to this Sudoku.
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...
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.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
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?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
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?
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?
Can you coach your rowing eight to win?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Given the products of adjacent cells, can you complete this Sudoku?
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the 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. . . .
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?
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. . . .
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
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.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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.
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?
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.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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?