Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you complete this jigsaw of the multiplication square?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
If you have only four weights, where could you place them in order to balance this equaliser?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Choose a symbol to put into the number sentence.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Can you hang weights in the right place to make the equaliser balance?
What happens when you try and fit the triomino pieces into these two grids?
An odd version of tic tac toe
Try out the lottery that is played in a far-away land. What is the chance of winning?
An environment which simulates working with Cuisenaire rods.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Can you cover the camel with these pieces?
Use the clues to colour each square.
Here is a chance to play a version of the classic Countdown Game.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Can you find all the different ways of lining up these Cuisenaire rods?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Use the number weights to find different ways of balancing the equaliser.
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.