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 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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
If you have only four weights, where could you place them in order
to balance this equaliser?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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 six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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!
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....?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
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?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
Can you complete this jigsaw of the multiplication square?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you hang weights in the right place to make the equaliser
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Use the clues to colour each square.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Choose a symbol to put into the number sentence.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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.
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?
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 find all the different ways of lining up these Cuisenaire
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Use the number weights to find different ways of balancing the equaliser.
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
What are the coordinates of the coloured dots that mark out the
tangram? Try changing the position of the origin. What happens to
the coordinates now?