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?
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.
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
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?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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.
This challenge extends the Plants investigation so now four or more children are involved.
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.
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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.
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?
A few extra challenges set by some young NRICH members.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
A challenging activity focusing on finding all possible ways of stacking rods.
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?
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?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Use the clues about the shaded areas to help solve this sudoku
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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?
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?
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
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.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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.
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
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.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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 letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?