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?"

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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?

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...

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?

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?

Given the products of adjacent cells, can you complete this Sudoku?

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.

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve 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"?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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.

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?

Given the products of diagonally opposite cells - can you complete this Sudoku?

Each clue number in this sudoku is the product of the two numbers in adjacent cells.

A few extra challenges set by some young NRICH members.

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.

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?

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

This Sudoku, based on differences. Using the one clue number can you find the solution?

You need to find the values of the stars before you can apply normal Sudoku rules.

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.

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?

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.

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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.

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?

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.

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.

The clues for this Sudoku are the product of the numbers in adjacent squares.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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?

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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?

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?

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.

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Solve the equations to identify the clue numbers in this Sudoku problem.

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?

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?

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?

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Find out about Magic Squares in this article written for students. Why are they magic?!