Given the set {1, 2, 3, ..., 144}, what is the largest subset of integers such that no three of the integers in the subset correspond to sides of a triangle?
Three integers can't form a triangle if the largest is greater than or equal to the sum of the other two.
If one starts with 1 and 2, the next can safely be 3. Then the next can safely be 5, etc., and we are forming the fibonacci series. There are 11 elements in this subset of the Fibonacci series:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
This would be the largest such set as starting anywhere else but 1 would result in fewer members.
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Posted by Charlie
on 2024-12-22 09:43:43 |
proposed solution