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

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

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?

A few extra challenges set by some young NRICH members.

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

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

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

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.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

A challenging activity focusing on finding all possible ways of stacking rods.

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

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

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

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.

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

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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?

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?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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?

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

Can you use the information to find out which cards I have used?

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

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

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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

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

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 focuses on finding the sum and difference of pairs of two-digit numbers.

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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?

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