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How many numbers in the end? (Posted on 2018-01-28) Difficulty: 3 of 5
Start with a set of a few distinct natural numbers.
For any 2 members, add their least common multiple to the set, if and only if it was not already in the set.
Continue the task until it cannot be done.
Call the result a final list.

a. (2,4,8,16) a is a final list.
b. (2,3,4,6) will become a final list once we add number 12 to the set.

What can be the longest final list, if the initial set had 10 distinct numbers?

No Solution Yet Submitted by Ady TZIDON    
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Solution D1 (spoiler) | Comment 1 of 2
2^10 - 1.

For instance, if the initial set had 10 primes, then the full set is the set of all products of the numbers in any non-empty subset of the 10 primes.

In general, n primes lead to a full set of 2^n - 1.

For instance, {2,3,5} generates a final set of {2,3,5,6,10,15,30}

Edited to reflect Ady's preferred wording

Edited on January 28, 2018, 6:58 pm
  Posted by Steve Herman on 2018-01-28 09:26:00

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