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?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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?"
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five 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.
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.
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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.
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.
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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 diagonally opposite cells - can you complete this Sudoku?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
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?
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
A pair of Sudoku puzzles that together lead to a complete solution.
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.
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?!
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
This Sudoku requires you to do some working backwards before working forwards.
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
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.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?