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. . . .

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

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?

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?"

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.

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

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

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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

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?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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

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?

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

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

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

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?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

A few extra challenges set by some young NRICH members.

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Have a go at balancing this equation. Can you find different ways of doing it?

Can you work out some different ways to balance this equation?

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.

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

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. . . .

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

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.

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

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

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

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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. . . .

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Use the differences to find the solution to this Sudoku.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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.

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

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

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.