Ring a Ring of Numbers
Stage: 1 Challenge Level: 
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
More Numbers in the Ring
Stage: 1 Challenge Level:
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?
Two and One
Stage: 1 Challenge Level:
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
Three Ball Line Up
Stage: 1 Challenge Level:
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Making Trains
Stage: 1 Challenge Level:
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?
Cuisenaire Counting
Stage: 1 Challenge Level:
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Same Length Trains
Stage: 1 Challenge Level:
How many trains can you make which are the same length as Matt's, using rods that are identical?
Number Balance
Stage: 1 Challenge Level:
Can you hang weights in the right place to make the equaliser balance?
Weighted Numbers
Stage: 1 Challenge Level:
Use the number weights to find different ways of balancing the equaliser.
Are You Well Balanced?
Stage: 1 Challenge Level:
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Getting the Balance
Stage: 1 Challenge Level:
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?
We'll Bang the Drum
Stage: 1 Challenge Level:
How many different rhythms can you make by putting two drums on the wheel?
Board Block
Stage: 1 Challenge Level:
Take it in turns to make a triangle on the pegboard. Can you block your opponent?
Inside Triangles
Stage: 1 Challenge Level:
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Carroll Diagrams
Stage: 1 Challenge Level:
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Overlaps
Stage: 1 Challenge Level:
What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.
Spot Thirteen
Stage: 2 Challenge Level:
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
All Change
Stage: 1 Challenge Level:
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?
Poly Plug Pattern
Stage: 1 Challenge Level:
Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?
NRICH is part of the family of activities in the Millennium Mathematics Project.