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Factor-multiple Chains

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Joel, Callum and Bethan from William Harding School each sent in a solution to this problem. They all agreed that the smallest blue numbers that make a complete chain are 2-4-8-16 and the largest blue numbers that will make a complete chain are 5-25-50-100. (Although what is the largest number possible in position one?)

Tiberiu wrote to us to say:

All prime numbers between 13 and 99 cannot be used in a chain.

I wonder if you can explain why? Are there some other numbers which can't appear?

Tiberiu continued:

Three numbers closest to 2 and the last one closest to 100 will give you the largest difference (between adjacent numbers) : 2,4,8,96. The largest difference in this case is 88.
The largest range: 2,10,50,100 range: 98
The smallest range: 2,4,8,16 range: 14

The "Southville Sizzlers" at Southville Primary School also worked hard on this problem. Well done to all of you.