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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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.
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?
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?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
A few extra challenges set by some young NRICH members.
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?"
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
A challenging activity focusing on finding all possible ways of stacking rods.
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?
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?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Two sudokus in one. Challenge yourself to make the necessary connections.
A Sudoku that uses transformations as supporting clues.
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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?
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?
A Sudoku with clues as ratios.
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?
Four small numbers give the clue to the contents of the four surrounding cells.
Given the products of adjacent cells, can you complete this Sudoku?