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.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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?
Four small numbers give the clue to the contents of the four surrounding cells.
A pair of Sudoku puzzles that together lead to a complete solution.
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?
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
A challenging activity focusing on finding all possible ways of stacking rods.
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
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.
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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.
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
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.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Use the differences to find the solution to this Sudoku.
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
Use the clues about the shaded areas to help solve this sudoku
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
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.
A few extra challenges set by some young NRICH members.
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 Sudoku based on clues that give the differences between adjacent cells.
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?
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?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
Solve the equations to identify the clue numbers in this Sudoku problem.
Find out about Magic Squares in this article written for students. Why are they magic?!
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. . . .
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
Two sudokus in one. Challenge yourself to make the necessary connections.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
How many different differences can you make?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
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.