Follow the clues to find the mystery number.
Have a go at balancing this equation. Can you find different ways of doing it?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
An investigation that gives you the opportunity to make and justify predictions.
The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
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?
Can you make square numbers by adding two prime numbers together?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
Can you replace the letters with numbers? Is there only one solution in each case?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you use the information to find out which cards I have used?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
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?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
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?
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.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Investigate the different ways you could split up these rooms so that you have double the number.
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
A few extra challenges set by some young NRICH members.
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?