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?
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?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
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.
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
A challenging activity focusing on finding all possible ways of stacking rods.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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.
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 challenge extends the Plants investigation so now four or more children are involved.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
You need to find the values of the stars before you can apply normal Sudoku rules.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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.
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.
A few extra challenges set by some young NRICH members.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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.
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.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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.
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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 find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Can you find all the different triangles on these peg boards, and find their angles?
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.
Can you find all the different ways of lining up these Cuisenaire rods?
This Sudoku, based on differences. Using the one clue number can you find the solution?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?