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Linda's Very Annoying Sticks
Linda has a collection of N sticks, all of integer length, with no two sticks having the same length. The shortest stick has a length of 1; the longest stick is not longer than 60. Linda is very annoyed with her collection of sticks because for any subset of three sticks it is impossible to form a triangle with them. What is the largest possible value of N ? (Random bonus problem: How many digits long is the 9999th Fibonacci number? Assume the first and second terms of the Fibonac
Feb 20, 2023, 1:36 pm - cottoneyedjoe - Mathematics Forum

Linda's Very Annoying SticksReply
Re :Fibonacci Numbers --The Fingerprint of God Blessings of Peace Hrmony
Feb 26, 2023, 7:37 pm - eddessaknight - Mathematics Forum

Linda's Very Annoying SticksReply
fibonacci # 0-1-1-2-3-5-8-13-21-34-55-89-144-233-377-610-987-1597-2584-4181- 2584-4181 ... ~ This is softer: 00-01-01-02-03-05-07-10-14-20-28-40-56
Feb 27, 2023, 5:33 pm - eddessaknight - Mathematics Forum

Linda's Very Annoying SticksReply
The bonus question is easier: 2090 digits. Didnt even have to use Wolfram Alpha to cheat! But I did ask someone smart for a hint and they said Binet Formula. B.F. says nth Fibonacci number is [ ^n - (-1/ )^n]/sqrt(5) Take the logarithm base 10 rounded up to the next whole number to get the length. That's where you need rules of logarithms and the realization that as n gets larger the term (-1/ )^n becomes practically 0. log_10(Binet Formula) = n*log_10( ) - log_10(sqrt(5)) Plug
Feb 22, 2023, 1:13 pm - db101 - Mathematics Forum

Linda's Very Annoying SticksReply
The largest possible value of N is 9. Any more than 9 sticks and Linda will be able to find at least one set of three that makes a triangle. I solved it like this. First, the only way that three lengths can form a triangle is if the longest length is less than the sum of the two shorter lengths. The shortest stick has a length of 1 and all the lengths are different, so I tried to find an increasing sequence of numbers where each successive term is at least as large as the sum of any two prev
Feb 23, 2023, 12:52 am - db101 - Mathematics Forum