A few extra challenges set by some young NRICH members.

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?

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

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

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

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

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?

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

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?

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

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. . . .

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

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.

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 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.

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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?"

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?

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?

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

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

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. . . .

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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

In this matching game, you have to decide how long different events take.

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

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?

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.

This challenge extends the Plants investigation so now four or more children are involved.

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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?

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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.

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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?

Try out the lottery that is played in a far-away land. What is the chance of winning?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?