Numbers Between the Pairs

Solution

There is a lot of solutions to this puzzle. Below we show some of your solutions with interesting comments.

Solution by Thiago Alexandre dos Santos

After a lot of thinking I finally solve this brain teaser. here's the answer:

8-9-10-11-12-13-14-15-16-8-7-9-3-10-5-11-3-12-7-13-5-14-6-15-2-16-4-2-1-6-1-4.
 

Solution by Lee Root

I solved this by putting the numbers in a spread sheet and solving like a jigsaw puzzle
1.1
2..2
3...3
16................16

my answer is...

8, 9, 10, 11, 12, 13, 14, 15, 16, 8, 7, 9, 3, 10, 5, 11, 3, 12, 7, 13, 5, 14, 4, 15, 6, 16, 2, 4, 1, 2, 1, 6.

Solution by Hennie van der Merwe

The correct answer is:

6; 8; 11; 16; 12; 3; 5; 6; 14; 3; 8; 13; 5; 4; 11; 15; 10; 12; 4; 9; 16; 2; 7; 14; 2; 13; 1; 10; 1; 9; 7; 15

Kept me out of work for a while. Thanks.

Solution by Big Trev

4, 6, 3, 5, 15, 4, 3, 14, 6, 5, 7, 16, 10, 13, 2, 9, 12, 2, 7, 11, 15, 8, 14, 10, 1, 9, 1, 13, 16, 12, 8, 11

You're right puzzles are great, but it'll be 1am before I get to bed and I have a busy day tomorrow!

Still, I have done it. 

Cheers for the puzzle...

Solution by Alan Lemm

I have so far found 183 solutions to this puzzle. Below are two of them:

16-14-15-4-8-13-5-12-4-1-11-1-5-8-9-10-14-16-15-13-12-7-11-6-9-2-10-3-2-7-6-3

16-14-15-7-8-13-1-12-1-5-10-7-9-8-11-5-14-16-15-13-12-10-9-6-4-2-11-3-2-4-6-3

Solution by NickyG

I found an order: 
9, 7, 10, 11, 12, 13, 14, 15, 16, 7, 9, 8, 5, 10, 1, 11, 1, 12, 5, 13, 8, 14, 6, 15, 3,1 6, 4, 2, 3, 6, 2, 4.

I doubt this is the only one, though. I can't see an easy way to do this - I started by taking the large numbers first, writing down 8,9,10,11,12,13,14,15,16,8,.,9,.,
10,.,11,.,12,.,13,.,14,.,15,.,16 (where dot is a gap) and tried to fill in the gaps with the smaller numbers with something like 7,.,6,.,5,.,4,.,7,6,5,4. I couldn't get that to work, so I moved the 8s from the larger to the smaller numbers and tried again. This didn't work so then I thought about putting numbers around the clump of consecutive numbers on the left hand side of the list of larger numbers (the 8-16 clump). I made this clump smaller (in my solution it is 10-16) so I could fit the 7s round it, and then the 9s around the 7s. Then I managed to fill the gaps with the leftover numbers. I seemed to find my solution a bit by chance, which makes me think there are others.