### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

# Factors and Multiples Game

##### Stage: 2, 3 and 4 Challenge Level:

At Montsaye Community College in Northamptonshire, Year 8 students have taken on the challenge of finding the longest sequence of numbers that can be crossed out.

Gabrielle and Lauren managed a sequence of 50 numbers:

Makenzie managed to improve on this with a chain of $55$ numbers:

Sophie and Tasmin managed to improve on that:

Gabrielle and Lauren managed to improve on their earlier effort:

And Sophie and Tasmin also managed to do even better!

Abigail from Ridgewood School also managed a chain of 61 numbers:

Alfie, Manuel, Jack and Emilio from Newhall School in Chelmsford, Essex, worked as a team to also produce a chain of 61:

A.H. from Manorfield Primary School has improved on this by finding a chain of $63$ numbers:

90-9-99-33-66-11-44-22-88-8-80-40-10-100-20-60-30-15-75-25-50-5-35-7-70-14-56-28-
84-21-42-6-78-39-13-26-52-4-68-34-17-51-1-46-92-23-69-3-57-19-38-76-2-24-72-18-
36-12-48-16-24-32-96

Evie from Deansfield Primary School created a chain of 65 numbers:

James from Ridgewood School showed he could do even better:

Linda from Bohunt School also used 68 numbers:

A group of Year 9 students from The Perse School for Girls in Cambridge worked together and managed an even longer chain of numbers:

And Claire, of Blackheath High School in London, has managed to improve on that:

Jacky, from Princethorpe College in Rugby, has managed to go one better with a chain of 74:

Jesse from Moriah College in Sydney, Australia also managed a chain of 74 numbers:

Well done to all of you. Do let us know if you can do any better!