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Fibonacci Question

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pinkee | 09:22 Mon 17th Oct 2022 | Quizzes & Puzzles
12 Answers

Please can someone help me with the following question:

Rearrange the numbers 1 to 12 so that the addition of every adjacent pair is a fibonacci number.
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4-9-12-1-7-6-2-11-10-3-5-8
well done JJ.
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Thank you Jonathan-Joe. I was really struggling with that one.

Doesn't it have to be alternating odd and even no.s; 21, 8 aren't fibonacci no.s
The Fibonacci sequence of whole numbers is: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584,...

2, 3, 4, 1, 6, 5, 8, 9, 10, 7, 12, 11

Sorry, talking absolute rubbish (not for the first time).

My solution is the rearrangement of 1-12 with adjacent numbers adding up to primes (should have read the rubric).
(1,12), (2,11), (3,10), (4,9), (5,8), (6,7)

The first digit in each pair increases by one and the second digit decreases by one.
can I ask you mathematical wonders how you did it
that is the algorithm that you used to generate the sequence

did ja gues at the first or was there a reason ( like it generates a sequence and the others dont)

or didja have the first eleven Fibonacci numbers in your mind and sort tho'

Poincare and Polya were interested in this: how to solve a problem and not its actual solution
I drew a 12 x 12 table, columns labelled 1 to 12, rows 1 to 12. In each cell I put the total of header + row where this is a Fibonacci number. We see straight away that in our solution 12 can be flanked only by 1 and 9, and then 11 only by 2 and 10. Looking at remaining numbers in succession we build up and join series of numbers.
I'd start with ---the numbers 1 to 12 add up to 78 so we need 6 pair's totaling 13 each.
I would then use the list of fibonachi numbers from Google or from some posts here

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