Fibonacci Question

[pinkee]

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.

[Jonathan-Joe]

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

[TheWinner]

well done JJ.

[pinkee]

Thank you Jonathan-Joe. I was really struggling with that one.

[drmorgans]

Doesn't it have to be alternating odd and even no.s; 21, 8 aren't fibonacci no.s

[elliemay1]

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,...

[drmorgans]

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

[drmorgans]

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

[drmorgans]

My solution is the rearrangement of 1-12 with adjacent numbers adding up to primes (should have read the rubric).

[THECORBYLOON]

(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.

[Peter Pedant]

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

[Jonathan-Joe]

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.

[bobbinwales]

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