A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
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.
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?
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?
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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 challenge extends the Plants investigation so now four or more children are involved.
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?
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 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.
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
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 six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
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.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
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.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
A challenging activity focusing on finding all possible ways of stacking rods.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
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?
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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 pair of Sudoku puzzles that together lead to a complete solution.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .
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.
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.
This Sudoku combines all four arithmetic operations.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
Given the products of adjacent cells, can you complete this Sudoku?