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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:
 

Abigail's solution


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

Newhall solution


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:
 
solution
 

Linda from Bohunt School also used 68 numbers:

 

 link

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

 

 Chain of 71

 

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!