Linda's Very Annoying Sticks

Reply #12

sully16 — Tue, 14 Mar 2023 18:34:14 GMT

Reply #11

db101 — Tue, 14 Mar 2023 16:38:29 GMT

She can start by getting the snakes and sticks out of her hair. I think that's the first lesson at Vidal Sassoon's school.

Reply #10

sully16 — Tue, 14 Mar 2023 00:29:56 GMT

Linda has a scalene triangle, and she's having a bad hair day.

Reply #9

eddessaknight — Mon, 27 Feb 2023 22:33:08 GMT

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

Reply #8

eddessaknight — Mon, 27 Feb 2023 00:37:31 GMT

Re :Fibonacci Numbers --The Fingerprint of God

Blessings of Peace Hrmony

Reply #7

db101 — Sun, 26 Feb 2023 20:57:44 GMT

Darn tootin you will! Jk, I like a good logic puzzle even with dumb old Linda and her sticks.

Reply #6

cottoneyedjoe — Fri, 24 Feb 2023 15:47:06 GMT

LOL. That's much more interesting. Cletus's Pillowcase Full of Uncooperative Snakes Puzzle has a nice ring to it. I'll run the titles by you from now on.

Reply #5

db101 — Fri, 24 Feb 2023 00:15:15 GMT

How about a variation where Linda is changed to Cletus and the sticks are replaced with snakes

Reply #4

cottoneyedjoe — Thu, 23 Feb 2023 15:58:12 GMT

Nice work on both solutions.

I was thinking about how to make interesting variations of the problem. Like replace triangle with quadrilateral. The only way 4 lengths can form a quadrilateral is if the longest is shorter than the sum of the other three. So a max-length increasing sequence would be

1, 2, 3, 6, 11, 20, 37

And the max would be 7.

Or, if you allowed some sticks to have the same length, then all you could do is start off any solution sequence with an extra 1

Reply #3

db101 — Thu, 23 Feb 2023 05:52:10 GMT

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... [ More ]

Reply #2

db101 — Wed, 22 Feb 2023 22:46:53 GMT

Ah now I see that the bonus question is a hint for the first question. Very tricky Joe! I'll post a solution later when I have more time.

Reply #1

db101 — Wed, 22 Feb 2023 18:13:45 GMT

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... [ More ]

Linda's Very Annoying Sticks

cottoneyedjoe — Mon, 20 Feb 2023 18:36:21 GMT

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... [ More ]