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?"

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

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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?

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...

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

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

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

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?

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?

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?

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?

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

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.

How many different symmetrical shapes can you make by shading triangles or squares?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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?

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.

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.

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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.

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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.

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?

Use the differences to find the solution to this Sudoku.

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

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

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

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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 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.

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

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?

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

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?

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?

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

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?

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

A challenging activity focusing on finding all possible ways of stacking rods.

Four small numbers give the clue to the contents of the four surrounding cells.

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?