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?
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 letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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?
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.
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.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
Given the products of adjacent cells, can you complete this Sudoku?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
A Sudoku that uses transformations as supporting clues.
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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?"
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.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Two sudokus in one. Challenge yourself to make the necessary connections.
A Sudoku with clues as ratios.
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.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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.
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 Sudoku with a twist.
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A Sudoku with clues as ratios or fractions.
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.
You need to find the values of the stars before you can apply normal Sudoku rules.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
A Sudoku with clues as ratios.