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

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.

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.

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?

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

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

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

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?"

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?

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?

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

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

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

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?

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?

A few extra challenges set by some young NRICH members.

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.

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?

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?

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.

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

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?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

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

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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.

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?

Use the clues about the shaded areas to help solve this sudoku

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

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.

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.

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!

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

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

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

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.

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

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 symmetrical shapes can you make by shading triangles or squares?