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. . . .

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

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?

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 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?

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?

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?

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

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?

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

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

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?

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.

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.

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.

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.

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?

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?

A Sudoku that uses transformations as supporting clues.

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

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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.

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.

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?

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

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. . . .

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

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

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?

A Sudoku with clues given as sums of entries.

Use the differences to find the solution to this Sudoku.

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

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

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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

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

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

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

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

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

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