### Round and Round the Circle

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

### Pumpkin Pie Problem

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

### The Moons of Vuvv

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

# Factor Lines

##### Stage: 2 and 3 Challenge Level:

If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.

Arrange the four number cards (1, 2, 3 and 21) on the grid above to make a diagonal, vertical or horizontal line.
You can put a number card on a square with
• the same number
• a multiple of that number
• a factor of that number.

In how many different ways can you do it? Can you use a strategy that you haven't tried before?

You can use the interactivity above orĀ this sheet. The interactivity keeps track of the number of different lines you have created and you can view the lines you've already made by clicking 'Show lines'.

This problem has been adapted from the book "Cards on the Table" by Fran Mosley, published by BEAM Education .