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This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you hang weights in the right place to make the equaliser balance?
Find all the numbers that can be made by adding the dots on two dice.
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.
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
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?
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?
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!
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
If you have only four weights, where could you place them in order to balance this equaliser?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Choose a symbol to put into the number sentence.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
These two group activities use mathematical reasoning - one is numerical, one geometric.
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
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?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
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!
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.