### 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?

### Bracelets

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

### Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

# Factors and Multiples Game

##### Age 7 to 16 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:

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

This solution came in from Ralph and Max at the Institut International de Lancy in Switzerland. Their teacher said they did not use a computer or calculator. They made a chain of 65, which seems to be a very popular answer.

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:

Izaak, from Hills Rd VI Form College, used some computer programming techniques to try to make the longest chain he could. Below is his 76 long chain. If you want to read about his program and see his code, he has shared it on Github.

Jakob from Haberdashers Adams School in the UK managed to go one further with a 77 long chain:

Well done to all of you. Do let us know if you can do any better - we don't know if it is possible to improve on 77!