Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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.
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?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Here is a chance to play a version of the classic Countdown Game.
If you have only four weights, where could you place them in order to balance this 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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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!
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Can you hang weights in the right place to make the equaliser balance?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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....?
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
An odd version of tic tac toe
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
An environment which simulates working with Cuisenaire rods.
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?
Use the number weights to find different ways of balancing the equaliser.
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 put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
How many trains can you make which are the same length as Matt's, using rods that are identical?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Find out what a "fault-free" rectangle is and try to make some of your own.
Choose a symbol to put into the number sentence.
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of these clocks?