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?
Given the products of adjacent cells, can you complete this Sudoku?
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 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?"
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
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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.
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?
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?
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 clues for this Sudoku are the product of the numbers in adjacent squares.
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?
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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.
A few extra challenges set by some young NRICH members.
Given the products of diagonally opposite cells - can you complete this Sudoku?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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 puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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?
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
This challenge extends the Plants investigation so now four or more children are involved.
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
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?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
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.
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.
Use the differences to find the solution to this Sudoku.
A challenging activity focusing on finding all possible ways of stacking rods.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
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?