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 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?
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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?
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 Sudoku, based on differences. Using the one clue number can you find the solution?
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.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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 NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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 investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Given the products of adjacent cells, can you complete this Sudoku?
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
Use the differences to find the solution to this Sudoku.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
The clues for this Sudoku are the product of the numbers in adjacent squares.
A few extra challenges set by some young NRICH members.
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?
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?
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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.
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?
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?"
Four small numbers give the clue to the contents of the four surrounding cells.
A Sudoku with a twist.
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
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 Sudoku with clues as ratios.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This challenge extends the Plants investigation so now four or more children are involved.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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.
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.