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. . . .

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.

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?"

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?

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

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

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

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

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 diagonally opposite cells - can you complete this Sudoku?

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

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

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?

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

A Sudoku based on clues that give the differences between adjacent cells.

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.

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

A pair of Sudoku puzzles that together lead to a complete solution.

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 Sudoku that uses transformations as supporting clues.

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.

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

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

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?

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

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.

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

A Sudoku with clues given as sums of entries.

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

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

Two sudokus in one. Challenge yourself to make the necessary connections.

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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?

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?

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

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?

This Sudoku requires you to do some working backwards before working forwards.

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

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

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.

Two sudokus in one. Challenge yourself to make the necessary connections.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

In this article, the NRICH team describe the process of selecting solutions for publication on the site.