I really need you guys. I’ve been on this for a few days now on and off. I cant solve it. Id love the answer but if theres some kind of strategy, Id love to know that too. Thanks TM.
Put the numbers in the circles to all add up to 35:
http://www.puzzleadventure.com/puzzles/starturn.gif
Good luck! 
Maybe 36?
The 12 numbers are 3 - 15; therefore the average number is 9.
Each sum is the sum of 4 numbers.
The number “12” isn’t present. (3-15 would be 13 numbers.) The average number is 105/12, which (times 4) would be 35.
bup is wrong, because 12 is not one of the numbers.
The numbers total to 105. Each number is counted twice (in two different lines) so the total of all lines is 210. Since there are six lines, 210/6 = 35, so the question is right.
There are two different kinds of nodes in that graph: The corner nodes are different from the middle nodes.
Well, there are 624 solutions, listed below. These are listed starting at the top node, then left to right the next four, and so on.
By the way, to bup, 35 does work, as they are 3 to 15, but 12 is not included. (12 nodes total).
Yes, I figured these all out by hand. not.
The answers:
3 4 5 15 11 14 8 13 7 6 9 10
3 4 5 15 11 14 10 13 9 6 7 8
3 4 9 14 8 10 7 13 6 5 11 15
3 4 11 15 5 8 10 13 9 6 7 14
3 4 13 7 11 14 10 5 9 6 15 8
3 4 13 10 8 14 7 5 6 9 15 11
3 4 13 11 7 9 15 10 14 5 6 8
3 4 15 11 5 8 14 9 13 6 7 10
3 5 6 10 14 15 9 11 7 4 13 8
3 5 8 15 7 10 13 14 11 6 4 9
3 5 11 13 6 7 10 14 8 4 9 15
3 5 11 15 4 14 8 7 6 13 9 10
3 5 13 7 10 15 11 4 9 8 14 6
3 5 13 10 7 15 8 4 6 11 14 9
3 5 15 11 4 10 8 7 6 9 13 14
3 6 4 14 11 13 10 15 7 5 8 9
3 6 4 14 11 15 8 13 5 7 10 9
3 6 5 15 9 14 7 13 4 8 10 11
3 6 7 9 13 14 8 11 5 4 15 10
3 6 7 13 9 10 8 15 5 4 11 14
3 6 7 13 9 10 14 15 11 4 5 8
3 6 8 14 7 15 13 9 10 11 5 4
3 6 9 13 7 8 14 15 11 4 5 10
3 6 13 11 5 10 7 9 4 8 14 15
3 6 15 5 9 10 14 7 11 4 13 8
3 7 6 14 8 15 13 11 9 10 5 4
3 7 10 13 5 8 15 14 11 6 4 9
3 7 11 13 4 15 9 6 5 14 10 8
3 7 13 9 6 14 8 5 4 11 15 10
3 7 14 8 6 13 15 5 11 10 9 4
3 7 15 8 5 13 10 4 6 11 14 9
3 8 10 13 4 7 14 15 9 6 5 11
3 8 14 4 9 11 15 7 10 5 13 6
3 8 14 6 7 13 15 5 10 9 11 4
3 8 14 9 4 7 10 11 5 6 13 15
3 9 4 14 8 15 11 13 5 10 7 6
3 9 5 15 6 14 10 13 4 11 7 8
3 9 11 5 10 15 13 6 7 8 14 4
3 9 13 7 6 8 10 11 4 5 15 14
3 9 13 7 6 14 10 5 4 11 15 8
3 9 15 5 6 7 14 10 8 4 13 11
3 10 5 11 9 13 15 14 8 7 6 4
3 10 7 13 5 11 15 14 8 9 4 6
3 10 9 5 11 15 13 8 6 7 14 4
3 11 5 9 10 13 15 14 7 6 8 4
3 11 7 13 4 10 14 15 6 9 5 8
3 11 14 4 6 8 15 10 7 5 13 9
3 11 14 4 6 10 13 8 5 7 15 9
3 11 15 5 4 8 14 9 6 7 13 10
3 11 15 5 4 10 14 7 6 9 13 8
3 13 9 7 6 8 14 15 4 5 11 10
3 14 10 6 5 9 15 13 4 7 11 8
4 3 5 14 13 15 7 11 8 6 10 9
4 3 5 14 13 15 9 11 10 6 8 7
4 3 9 10 13 14 6 8 7 5 15 11
4 3 11 8 13 15 9 5 10 6 14 7
4 3 13 9 10 11 14 7 15 5 8 6
4 3 13 14 5 7 9 11 10 6 8 15
4 3 13 14 5 10 6 8 7 9 11 15
4 3 15 8 9 11 13 5 14 6 10 7
4 5 8 7 15 14 11 9 10 3 13 6
4 5 10 9 11 13 15 8 14 6 7 3
4 5 11 10 9 13 15 7 14 8 6 3
4 5 14 13 3 6 10 11 9 7 8 15
4 5 14 13 3 9 7 8 6 10 11 15
4 5 15 6 9 13 11 3 10 8 14 7
4 5 15 8 7 6 14 10 13 3 9 11
4 5 15 9 6 13 8 3 7 11 14 10
4 6 7 8 14 15 13 9 11 5 10 3
4 6 8 11 10 9 7 14 5 3 13 15
4 6 8 11 10 9 15 14 13 3 5 7
4 6 9 15 5 8 13 14 11 7 3 10
4 6 10 5 14 13 11 8 9 3 15 7
4 6 10 11 8 7 15 14 13 3 5 9
4 6 14 5 10 9 15 8 13 3 11 7
4 7 3 14 11 13 8 15 5 6 9 10
4 7 8 11 9 10 6 13 3 5 14 15
4 7 8 15 5 14 6 9 3 13 10 11
4 7 13 6 9 15 11 3 8 10 14 5
4 8 3 14 10 15 11 13 7 9 6 5
4 8 6 7 14 15 13 10 9 5 11 3
4 8 11 10 6 15 7 5 3 13 14 9
4 8 14 3 10 11 13 6 9 5 15 7
4 9 6 13 7 11 15 14 10 8 3 5
4 9 6 15 5 11 13 14 8 10 3 7
4 9 8 15 3 13 11 10 6 14 5 7
4 9 10 11 5 15 13 6 8 14 7 3
4 9 11 8 7 6 10 14 5 3 13 15
4 10 3 14 8 13 11 15 5 9 6 7
4 10 5 14 6 15 9 11 3 13 8 7
4 10 9 13 3 14 11 8 5 15 7 6
4 10 11 8 6 7 9 13 3 5 14 15
4 10 11 8 6 15 9 5 3 13 14 7
4 10 14 3 8 11 15 6 9 7 13 5
4 11 9 10 5 15 13 7 6 14 8 3
4 11 14 3 7 8 13 9 6 5 15 10
4 13 8 11 3 9 15 14 6 10 5 7
4 13 10 9 3 6 14 15 5 7 8 11
4 13 14 5 3 7 15 10 6 8 11 9
4 13 14 5 3 9 15 8 6 10 11 7
4 14 5 10 6 11 13 15 3 9 8 7
4 14 7 6 8 13 15 11 5 9 10 3
4 14 8 7 6 13 15 10 5 11 9 3
4 15 7 8 5 11 14 13 3 10 9 6
5 3 6 15 11 10 7 14 9 4 8 13
5 3 8 10 14 15 11 7 13 6 9 4
5 3 11 7 14 13 8 6 10 4 15 9
5 3 11 14 7 15 6 4 8 13 10 9
5 3 13 15 4 7 9 10 11 8 6 14
5 3 13 15 4 10 6 7 8 11 9 14
5 3 15 10 7 11 6 4 8 9 14 13
5 4 8 14 9 7 10 15 11 3 6 13
5 4 10 13 8 9 14 11 15 6 3 7
5 4 11 13 7 10 14 9 15 8 3 6
5 4 14 6 11 13 9 3 10 7 15 8
5 4 14 9 8 13 6 3 7 10 15 11
5 4 15 6 10 8 13 7 14 3 11 9
5 4 15 13 3 6 10 9 11 8 7 14
5 4 15 13 3 9 7 6 8 11 10 14
5 6 3 11 15 14 9 13 8 4 10 7
5 6 9 7 13 11 15 10 14 3 8 4
5 7 3 15 10 13 6 14 4 8 9 11
5 7 3 15 10 13 11 14 9 8 4 6
5 7 10 15 3 6 11 14 9 8 4 13
5 7 13 11 4 14 10 3 8 15 9 6
5 7 14 4 10 13 11 3 9 8 15 6
5 7 14 11 3 6 15 10 13 8 4 9
5 7 15 3 10 9 13 6 11 4 14 8
5 8 3 9 15 14 10 13 7 4 11 6
5 8 4 10 13 15 6 11 3 7 14 9
5 8 4 14 9 11 6 15 3 7 10 13
5 8 4 14 9 11 13 15 10 7 3 6
5 8 6 10 11 9 7 15 4 3 13 14
5 8 7 9 11 10 6 13 3 4 15 14
5 8 9 14 4 6 13 15 10 7 3 11
5 8 13 10 4 14 9 3 6 15 11 7
5 8 15 3 9 11 13 4 10 7 14 6
5 9 3 15 8 13 11 14 7 10 4 6
5 9 14 4 8 6 11 10 7 3 15 13
5 9 14 4 8 13 11 3 7 10 15 6
5 9 14 8 4 10 7 6 3 11 15 13
5 10 3 15 7 13 9 14 4 11 6 8
5 10 4 14 7 11 13 15 8 9 3 6
5 10 6 15 4 13 8 11 3 14 7 9
5 10 15 3 7 6 13 9 8 4 14 11
5 10 15 3 7 11 13 4 8 9 14 6
5 11 6 14 4 9 13 15 7 10 3 8
5 11 9 7 8 6 10 15 4 3 13 14
5 11 10 6 8 7 9 13 3 4 15 14
5 11 15 6 3 7 10 8 4 9 14 13
5 13 7 9 6 15 11 8 3 14 10 4
5 13 10 4 8 6 15 14 7 3 11 9
5 14 7 11 3 8 13 15 4 10 6 9
5 14 10 8 3 11 15 9 6 13 7 4
5 15 9 3 8 10 14 11 4 7 13 6
5 15 11 3 6 9 14 10 4 8 13 7
6 3 4 13 15 14 7 11 10 5 9 8
6 3 4 15 13 14 5 11 8 7 9 10
6 3 5 14 13 15 4 9 7 8 11 10
6 3 7 10 15 13 5 9 8 4 14 11
6 3 7 10 15 13 11 9 14 4 8 5
6 3 7 14 11 9 5 13 8 4 10 15
6 3 8 15 9 14 10 7 13 11 4 5
6 3 9 8 15 13 11 7 14 4 10 5
6 3 13 10 9 11 4 5 7 8 15 14
6 3 15 10 7 5 11 9 14 4 8 13
6 4 7 15 9 8 11 14 13 5 3 10
6 4 8 9 14 11 5 10 7 3 15 13
6 4 8 9 14 11 13 10 15 3 7 5
6 4 9 8 14 15 11 5 13 7 10 3
6 4 10 7 14 11 13 8 15 3 9 5
6 4 10 13 8 5 9 14 11 3 7 15
6 4 14 9 8 5 13 10 15 3 7 11
6 5 3 14 13 11 8 15 9 4 7 10
6 5 9 11 10 7 14 13 15 3 4 8
6 7 5 15 8 11 4 13 3 9 10 14
6 7 9 11 8 5 14 15 13 3 4 10
6 7 9 11 8 15 4 5 3 13 14 10
6 7 10 5 13 11 15 8 14 4 9 3
6 7 10 15 3 11 5 8 4 14 9 13
6 7 15 5 8 11 14 3 13 9 10 4
6 8 5 15 7 14 11 10 9 13 3 4
6 8 9 14 4 13 5 7 3 15 10 11
6 8 11 9 7 4 15 14 13 3 5 10
6 8 11 9 7 14 5 4 3 13 15 10
6 8 13 10 4 9 5 7 3 11 14 15
6 8 15 5 7 4 11 10 9 3 13 14
6 9 10 3 13 14 11 5 8 7 15 4
6 9 10 13 3 4 11 15 8 7 5 14
6 9 15 7 4 11 8 3 5 13 14 10
6 9 15 8 3 10 14 4 11 13 7 5
6 10 11 9 5 14 7 4 3 15 13 8
6 11 4 7 13 10 14 15 9 3 8 5
6 11 14 7 3 5 9 10 4 8 13 15
6 13 3 10 9 11 14 15 7 8 5 4
6 13 5 10 7 15 11 9 4 14 8 3
6 13 7 4 11 14 10 8 3 9 15 5
6 13 14 3 5 8 11 7 4 9 15 10
6 13 14 5 3 4 15 11 8 7 9 10
6 13 15 4 3 5 14 9 7 8 11 10
6 14 7 10 4 13 11 9 3 15 8 5
6 14 8 9 4 11 15 10 7 13 5 3
6 14 9 8 4 5 11 15 3 7 10 13
6 14 9 8 4 13 11 7 3 15 10 5
6 15 8 9 3 11 13 10 4 14 7 5
6 15 10 7 3 5 13 14 4 8 9 11
6 15 10 7 3 11 13 8 4 14 9 5
6 15 13 4 3 7 14 9 5 10 11 8
7 3 6 15 11 14 9 8 13 10 4 5
7 3 10 8 14 13 11 5 15 6 9 4
7 3 11 15 6 13 5 4 9 14 8 10
7 3 13 14 5 9 4 6 8 11 10 15
7 3 14 13 5 8 11 6 15 10 4 9
7 3 15 13 4 8 6 5 10 11 9 14
7 4 3 13 15 14 5 11 8 6 10 9
7 4 8 10 13 11 3 9 6 5 15 14
7 4 8 14 9 15 3 5 6 13 11 10
7 4 13 15 3 6 8 9 11 10 5 14
7 5 3 13 14 15 4 10 6 8 11 9
7 5 3 13 14 15 9 10 11 8 6 4
7 5 10 6 14 15 9 3 11 8 13 4
7 5 13 14 3 11 8 4 10 15 6 9
7 5 14 6 10 11 13 3 15 8 9 4
7 5 14 13 3 4 9 10 11 8 6 15
7 5 15 9 6 3 11 10 13 4 8 14
7 6 5 11 13 15 3 8 4 9 14 10
7 6 9 5 15 11 13 8 14 3 10 4
7 6 9 15 5 11 3 8 4 13 10 14
7 6 10 11 8 5 14 13 15 4 3 9
7 6 10 11 8 15 4 3 5 14 13 9
7 6 15 11 3 5 13 8 14 9 4 10
7 8 6 10 11 9 4 13 3 5 14 15
7 8 6 10 11 9 15 13 14 5 3 4
7 8 9 3 15 13 11 6 10 5 14 4
7 8 11 10 6 4 15 13 14 5 3 9
7 8 11 10 6 14 5 3 4 15 13 9
7 8 13 3 11 9 15 6 14 5 10 4
7 9 4 8 14 13 5 11 3 6 15 10
7 9 14 8 4 3 15 11 13 6 5 10
7 10 4 6 15 11 8 13 5 3 14 9
7 10 4 8 13 9 14 15 11 3 6 5
7 10 5 9 11 8 6 15 3 4 13 14
7 10 6 14 5 13 11 9 8 15 3 4
7 11 3 13 8 15 9 10 5 14 6 4
7 11 9 5 10 6 8 13 4 3 15 14
7 11 10 6 8 4 9 14 5 3 13 15
7 11 10 6 8 15 9 3 5 14 13 4
7 11 15 6 3 9 14 4 10 13 8 5
7 13 8 4 10 14 9 6 3 11 15 5
7 13 10 8 4 3 11 15 5 6 9 14
7 13 11 5 6 3 15 14 9 4 8 10
7 14 6 10 5 9 15 13 8 11 3 4
7 14 8 4 9 5 13 15 6 3 11 10
7 14 8 10 3 11 13 9 6 15 5 4
7 14 13 3 5 4 15 11 8 6 10 9
7 14 13 3 5 9 15 6 8 11 10 4
7 15 3 9 8 11 13 14 5 10 6 4
7 15 5 9 6 13 11 10 3 14 8 4
7 15 6 4 10 8 11 14 3 5 13 9
7 15 13 3 4 5 14 10 6 8 11 9
8 3 10 7 15 13 9 4 14 6 11 5
8 3 14 7 11 9 5 4 10 6 15 13
8 3 14 11 7 4 10 9 15 5 6 13
8 3 14 13 5 6 10 7 15 9 4 11
8 4 3 15 13 14 7 10 11 9 5 6
8 4 6 15 10 7 9 14 13 5 3 11
8 4 11 15 5 10 3 6 7 13 9 14
8 4 14 11 6 3 9 10 13 5 7 15
8 5 3 14 13 9 7 15 10 4 6 11
8 5 4 11 15 14 3 9 6 7 13 10
8 5 4 11 15 14 10 9 13 7 6 3
8 5 4 15 11 10 3 13 6 7 9 14
8 5 6 9 15 10 4 11 7 3 14 13
8 5 7 10 13 9 3 11 6 4 14 15
8 5 9 6 15 14 10 4 13 7 11 3
8 5 13 14 3 10 6 4 9 15 7 11
8 5 15 11 4 3 10 9 13 7 6 14
8 6 5 14 10 15 9 7 11 13 4 3
8 6 9 13 7 14 3 4 5 15 11 10
8 6 11 4 14 9 13 7 15 3 10 5
8 6 11 14 4 9 3 7 5 13 10 15
8 6 13 9 7 10 3 4 5 11 15 14
8 6 15 4 10 5 9 7 11 3 14 13
8 7 6 9 13 10 3 11 4 5 15 14
8 7 6 9 13 10 14 11 15 5 4 3
8 7 9 13 6 3 10 15 11 5 4 14
8 7 11 4 13 10 14 6 15 5 9 3
8 7 11 14 3 10 4 6 5 15 9 13
8 7 13 9 6 3 14 11 15 5 4 10
8 9 4 7 15 10 6 13 5 3 14 11
8 9 5 10 11 7 14 15 13 4 3 6
8 10 4 15 6 9 5 14 3 11 7 13
8 10 14 5 6 9 15 4 13 11 7 3
8 10 15 6 4 9 7 3 5 13 14 11
8 11 7 4 13 15 9 5 6 10 14 3
8 11 7 14 3 5 9 15 6 10 4 13
8 11 10 5 9 14 7 3 4 13 15 6
8 11 15 4 5 3 10 9 7 6 13 14
8 13 4 7 11 9 15 14 10 6 5 3
8 13 4 11 7 14 10 9 5 15 6 3
8 13 9 6 7 3 10 15 5 4 11 14
8 13 9 6 7 14 10 4 5 15 11 3
8 13 10 7 5 3 9 14 4 6 11 15
8 13 14 3 5 7 9 6 4 10 15 11
8 13 15 3 4 7 14 5 9 11 10 6
8 14 4 11 6 13 9 10 3 15 7 5
8 15 6 9 5 10 14 11 7 13 4 3
8 15 7 4 9 6 10 14 3 5 13 11
8 15 7 10 3 9 13 11 6 14 4 5
8 15 9 6 5 4 10 14 3 7 11 13
8 15 11 4 5 3 14 13 7 6 9 10
8 15 11 4 5 10 14 6 7 13 9 3
9 3 4 15 13 14 5 8 11 10 6 7
9 3 5 14 13 15 4 6 10 11 8 7
9 3 11 15 6 5 7 10 13 8 4 14
9 3 13 8 11 7 4 6 10 5 14 15
9 3 13 14 5 7 4 6 10 11 8 15
9 3 15 7 10 5 8 6 14 4 11 13
9 4 6 11 14 13 10 7 15 8 5 3
9 4 6 11 14 15 8 5 13 10 7 3
9 4 8 13 10 15 6 3 11 14 7 5
9 4 10 15 6 11 8 5 13 14 3 7
9 4 11 6 14 8 5 7 10 3 15 13
9 5 3 13 14 15 7 8 11 10 6 4
9 5 14 6 10 4 7 8 11 3 13 15
9 5 14 10 6 8 3 4 7 11 13 15
9 5 14 13 3 4 7 8 11 10 6 15
9 6 10 4 15 13 8 3 11 7 14 5
9 6 10 14 5 3 8 13 11 7 4 15
9 6 15 10 4 8 11 3 14 13 5 7
9 6 15 11 3 7 5 4 8 13 10 14
9 7 4 13 11 8 3 14 5 6 10 15
9 7 14 3 11 8 13 4 15 6 10 5
9 8 4 10 13 7 5 15 6 3 11 14
9 8 5 7 15 10 13 11 14 4 6 3
9 10 6 8 11 5 14 15 13 3 4 7
9 10 6 8 11 7 4 13 3 5 14 15
9 10 6 8 11 7 15 13 14 5 3 4
9 10 6 8 11 15 4 5 3 13 14 7
9 10 6 14 5 7 4 13 3 11 8 15
9 10 7 5 13 8 15 11 14 4 6 3
9 10 7 15 3 8 5 11 4 14 6 13
9 10 13 8 4 6 15 7 14 11 3 5
9 11 3 7 14 15 6 8 4 10 13 5
9 11 3 14 7 13 8 10 6 15 4 5
9 11 8 6 10 4 7 14 5 3 13 15
9 11 8 6 10 4 15 14 13 3 5 7
9 11 8 6 10 14 5 4 3 13 15 7
9 11 8 6 10 15 7 3 5 14 13 4
9 11 8 13 3 4 7 14 5 10 6 15
9 11 13 4 7 3 8 10 6 5 14 15
9 13 5 3 14 11 8 10 4 6 15 7
9 13 5 7 10 15 8 6 4 14 11 3
9 13 10 4 8 5 7 11 3 6 15 14
9 13 14 5 3 4 15 8 11 10 6 7
9 13 15 4 3 5 14 6 10 11 8 7
9 14 3 5 13 8 11 15 6 4 10 7
9 14 6 11 4 5 8 15 3 10 7 13
9 14 7 3 11 6 15 13 10 4 8 5
9 14 11 6 4 8 15 7 10 13 5 3
9 14 11 6 4 10 13 5 8 15 7 3
9 14 13 3 5 7 15 6 10 11 8 4
9 15 4 10 6 8 13 14 7 11 3 5
9 15 7 5 8 13 10 6 4 14 11 3
10 3 5 13 14 11 8 9 15 7 4 6
10 3 7 11 14 13 8 5 15 9 6 4
10 3 9 15 8 5 6 11 13 7 4 14
10 4 3 13 15 14 5 8 11 9 7 6
10 4 5 15 11 14 3 6 9 13 7 8
10 4 9 14 8 13 5 3 11 15 6 7
10 4 11 7 13 8 3 6 9 5 15 14
10 4 11 15 5 8 3 6 9 13 7 14
10 4 14 11 6 3 9 8 15 7 5 13
10 5 3 13 14 15 4 7 9 11 8 6
10 5 4 11 15 14 8 7 13 9 6 3
10 5 6 13 11 15 3 4 8 14 9 7
10 5 15 6 9 3 8 7 13 4 11 14
10 5 15 11 4 3 8 7 13 9 6 14
10 6 11 14 4 9 3 5 7 15 8 13
10 7 4 9 15 8 11 13 14 3 5 6
10 7 4 11 13 6 5 15 8 3 9 14
10 7 5 8 15 9 3 11 6 4 14 13
10 7 6 13 9 14 8 5 11 15 4 3
10 8 4 9 14 15 3 6 5 11 13 7
10 8 14 9 4 5 13 6 15 11 3 7
10 8 15 9 3 6 5 4 7 13 11 14
10 9 6 5 15 8 13 11 14 3 7 4
10 9 6 7 13 8 3 11 4 5 15 14
10 9 6 7 13 8 14 11 15 5 4 3
10 9 6 7 13 14 3 5 4 11 15 8
10 9 6 15 5 8 3 11 4 13 7 14
10 9 7 8 11 5 14 13 15 4 3 6
10 9 7 8 11 15 4 3 5 14 13 6
10 9 13 6 7 8 14 4 15 11 5 3
10 11 3 6 15 13 5 9 4 8 14 7
10 11 5 4 15 14 8 6 7 9 13 3
10 11 8 7 9 4 15 13 14 5 3 6
10 11 8 7 9 14 5 3 4 15 13 6
10 11 13 6 5 3 15 9 14 8 4 7
10 11 15 5 4 3 14 7 13 9 6 8
10 13 7 6 9 3 8 15 5 4 11 14
10 13 7 6 9 3 14 15 11 4 5 8
10 13 7 6 9 14 8 4 5 15 11 3
10 13 7 11 4 3 8 15 5 9 6 14
10 13 11 4 7 5 6 9 3 8 15 14
10 14 9 4 8 3 15 13 11 5 6 7
10 14 11 7 3 8 13 6 9 15 5 4
10 14 13 3 5 4 15 8 11 9 7 6
10 14 13 5 3 8 11 4 7 15 9 6
10 15 4 5 11 8 14 13 9 7 6 3
10 15 5 6 9 13 8 7 3 14 11 4
10 15 6 3 11 5 13 14 8 4 9 7
10 15 8 5 7 3 9 14 4 6 11 13
10 15 9 4 7 11 8 5 3 14 13 6
10 15 11 4 5 8 14 6 9 13 7 3
10 15 13 3 4 5 14 7 9 11 8 6
11 3 5 13 14 9 7 10 15 6 4 8
11 3 7 10 15 13 6 4 14 9 8 5
11 3 14 8 10 4 7 6 15 5 9 13
11 3 14 10 8 4 5 6 13 7 9 15
11 3 15 8 9 5 6 4 14 7 10 13
11 3 15 10 7 5 6 4 14 9 8 13
11 4 9 15 7 10 6 5 13 14 3 8
11 4 14 8 9 3 6 7 13 5 10 15
11 5 6 9 15 14 7 4 13 10 8 3
11 5 9 6 15 7 4 8 10 3 14 13
11 5 10 7 13 6 3 8 9 4 14 15
11 5 15 7 8 6 4 3 10 9 13 14
11 6 4 10 15 7 9 13 14 3 5 8
11 6 14 5 10 7 4 3 9 8 15 13
11 7 3 15 10 13 5 8 9 14 4 6
11 7 9 6 13 5 4 10 8 3 14 15
11 7 10 4 14 6 5 8 9 3 15 13
11 7 10 15 3 6 5 8 9 14 4 13
11 7 15 9 4 6 10 3 14 13 5 8
11 8 7 5 15 14 6 3 9 10 13 4
11 8 7 15 5 4 6 13 9 10 3 14
11 8 10 14 3 5 4 9 7 13 6 15
11 8 15 3 9 4 7 5 10 6 14 13
11 9 3 13 10 14 6 7 8 15 5 4
11 9 3 15 8 7 4 14 6 10 5 13
11 9 8 4 14 6 5 10 7 3 15 13
11 9 8 4 14 6 13 10 15 3 7 5
11 9 8 4 14 13 5 3 7 10 15 6
11 9 8 14 4 6 3 10 5 13 7 15
11 9 8 15 3 6 5 10 7 14 4 13
11 9 13 3 10 4 6 7 8 5 15 14
11 10 3 13 9 6 4 15 5 8 7 14
11 10 5 14 6 4 7 15 8 9 3 13
11 10 8 4 13 7 14 9 15 5 6 3
11 10 8 14 3 7 4 9 5 15 6 13
11 10 13 3 9 6 14 5 15 8 7 4
11 10 15 3 7 5 13 4 14 9 8 6
11 13 4 8 10 14 7 6 5 15 9 3
11 13 5 3 14 10 6 9 4 7 15 8
11 13 6 9 7 4 5 14 3 8 10 15
11 13 7 10 5 3 6 14 4 9 8 15
11 14 3 5 13 6 10 15 7 4 9 8
11 14 4 8 9 5 6 15 3 7 10 13
11 14 4 8 9 5 13 15 10 7 3 6
11 14 4 8 9 13 6 7 3 15 10 5
11 14 4 10 7 5 6 15 3 9 8 13
11 14 13 5 3 7 9 4 6 15 10 8
11 15 5 7 8 6 14 13 10 9 3 4
11 15 6 9 5 4 7 14 3 10 8 13
11 15 9 6 5 7 14 8 10 13 4 3
11 15 10 4 6 9 7 5 3 14 13 8
11 15 10 7 3 6 13 8 9 14 4 5
13 3 9 8 15 7 4 6 14 5 10 11
13 4 8 9 14 11 6 3 15 10 7 5
13 4 10 6 15 9 5 3 14 7 11 8
13 4 14 7 10 5 6 3 15 8 9 11
13 4 14 9 8 5 6 3 15 10 7 11
13 5 7 15 8 9 3 6 11 14 4 10
13 5 10 6 14 4 7 8 15 3 9 11
13 6 3 11 15 10 7 9 14 8 4 5
13 6 5 15 9 10 4 7 11 14 3 8
13 6 7 14 8 4 3 11 10 9 5 15
13 6 14 4 11 5 8 3 15 7 10 9
13 6 14 8 7 3 4 5 11 9 10 15
13 6 15 5 9 4 7 3 14 8 10 11
13 7 8 14 6 4 3 10 9 11 5 15
13 7 10 3 15 8 5 4 11 6 14 9
13 7 11 3 14 5 9 6 15 4 10 8
13 8 4 9 14 7 10 11 15 6 3 5
13 8 4 14 9 11 5 7 10 15 3 6
13 8 9 3 15 6 5 7 10 4 14 11
13 8 9 14 4 6 5 7 10 15 3 11
13 8 10 3 14 7 4 5 9 6 15 11
13 8 14 7 6 3 4 5 9 10 11 15
13 8 15 7 5 3 9 4 14 11 6 10
13 9 5 11 10 3 4 14 8 6 7 15
13 9 5 15 6 7 4 10 8 14 3 11
13 9 10 5 11 4 3 8 7 6 14 15
13 9 14 4 8 5 11 3 15 10 7 6
13 9 15 5 6 4 10 3 14 11 7 8
13 10 7 3 15 6 5 9 8 4 14 11
13 10 7 3 15 6 11 9 14 4 8 5
13 10 7 3 15 11 5 4 8 9 14 6
13 10 7 14 4 6 5 9 8 15 3 11
13 10 11 5 9 4 3 7 6 8 14 15
13 11 4 14 6 8 5 10 7 15 3 9
13 11 5 10 9 3 4 14 6 7 8 15
13 11 6 4 14 9 3 7 5 8 15 10
13 11 7 3 14 10 4 5 6 9 15 8
13 14 3 7 11 4 10 15 9 6 5 8
13 14 3 10 8 4 7 15 6 9 5 11
13 14 3 11 7 9 5 10 4 15 6 8
13 14 4 6 11 3 9 15 8 5 7 10
13 14 6 10 5 7 4 9 3 15 8 11
13 14 9 4 8 10 7 3 6 15 11 5
13 14 9 8 4 6 11 7 10 15 3 5
13 15 3 7 10 5 6 14 4 8 9 11
13 15 3 7 10 5 11 14 9 8 4 6
13 15 3 7 10 11 6 8 4 14 9 5
13 15 3 9 8 5 6 14 4 10 7 11
13 15 3 10 7 5 8 14 6 11 4 9
13 15 6 10 4 5 9 11 7 14 3 8
13 15 8 9 3 4 7 10 5 14 6 11
13 15 11 3 6 7 10 4 8 14 9 5
14 3 10 9 13 6 4 5 15 7 8 11
14 4 5 11 15 10 3 6 13 9 7 8
14 4 7 13 11 6 5 8 15 9 3 10
14 4 8 13 10 7 5 6 15 11 3 9
14 5 7 8 15 11 4 3 13 10 9 6
14 5 10 11 9 8 6 3 15 13 4 7
14 6 7 13 9 10 3 4 11 15 5 8
14 6 8 11 10 9 7 4 15 13 3 5
14 6 9 5 15 8 3 4 11 7 13 10
14 6 9 13 7 8 3 4 11 15 5 10
14 7 6 9 13 10 8 5 15 11 4 3
14 7 8 5 15 4 6 9 13 3 10 11
14 7 8 11 9 10 6 3 13 15 4 5
14 7 13 4 11 3 8 5 15 6 9 10
14 7 13 9 6 3 8 5 15 11 4 10
14 8 4 13 10 11 3 6 9 15 5 7
14 9 3 8 15 5 6 13 11 4 7 10
14 9 6 5 15 11 3 4 8 10 13 7
14 9 7 6 13 3 10 11 15 4 5 8
14 9 11 8 7 6 10 4 15 13 3 5
14 9 11 10 5 6 8 4 13 15 3 7
14 9 13 7 6 3 10 5 15 11 4 8
14 10 9 3 13 4 11 8 15 5 7 6
14 10 11 8 6 7 9 3 13 15 4 5
14 10 13 4 8 3 11 5 15 9 6 7
14 10 13 8 4 5 7 3 11 15 6 9
14 11 3 6 15 5 7 13 10 4 8 9
14 11 4 5 15 8 3 9 6 7 13 10
14 11 4 5 15 8 10 9 13 7 6 3
14 11 4 5 15 10 3 7 6 9 13 8
14 11 4 13 7 8 3 9 6 15 5 10
14 11 13 7 4 5 6 3 9 15 8 10
14 13 3 4 15 7 9 11 10 6 8 5
14 13 3 4 15 10 6 8 7 9 11 5
14 13 3 9 10 11 4 7 5 15 8 6
14 13 4 3 15 6 8 11 9 5 10 7
14 13 6 7 9 10 3 5 4 15 11 8
14 13 9 6 7 8 10 4 11 15 5 3
14 13 9 10 3 4 6 8 7 15 5 11
14 15 3 4 13 8 6 10 5 9 11 7
14 15 4 3 13 6 10 11 9 7 8 5
14 15 4 3 13 9 7 8 6 10 11 5
14 15 5 4 11 3 8 13 7 6 9 10
14 15 5 4 11 3 10 13 9 6 7 8
14 15 5 4 11 10 8 6 7 13 9 3
14 15 5 6 9 3 11 13 10 8 4 7
14 15 5 8 7 6 4 10 3 13 9 11
14 15 5 9 6 3 8 13 7 11 4 10
14 15 6 3 11 7 5 8 4 10 13 9
14 15 8 3 9 6 5 7 4 11 13 10
14 15 8 7 5 4 11 9 10 13 3 6
14 15 11 5 4 3 10 7 9 13 6 8
15 4 7 11 13 8 3 5 14 10 6 9
15 5 9 10 11 3 4 8 14 7 6 13
15 5 11 9 10 3 4 6 14 8 7 13
15 6 8 11 10 9 4 3 13 14 5 7
15 6 10 5 14 7 4 3 13 8 11 9
15 6 10 11 8 7 4 3 13 14 5 9
15 6 13 7 9 4 5 3 14 10 8 11
15 7 3 11 14 9 5 8 13 10 4 6
15 7 5 13 10 9 3 6 11 14 4 8
15 7 6 8 14 4 3 10 11 5 9 13
15 7 13 5 10 3 6 4 14 8 9 11
15 8 6 10 11 9 7 5 14 13 3 4
15 8 7 6 14 4 3 9 10 5 11 13
15 8 7 9 11 10 6 3 13 14 5 4
15 8 9 4 14 6 3 5 10 7 13 11
15 8 11 3 13 4 7 5 14 6 10 9
15 8 11 10 6 4 7 5 14 13 3 9
15 9 4 8 14 10 7 6 13 11 5 3
15 9 7 13 6 5 4 8 10 14 3 11
15 10 4 8 13 5 9 11 14 7 3 6
15 10 5 13 7 6 3 9 8 14 4 11
15 10 6 5 14 3 8 11 13 4 7 9
15 10 8 3 14 5 4 7 9 6 13 11
15 10 9 11 5 4 3 7 8 14 6 13
15 10 11 8 6 4 9 5 14 13 3 7
15 10 13 5 7 3 9 4 14 11 6 8
15 11 5 6 13 7 10 8 14 9 4 3
15 11 6 4 14 9 3 5 7 10 13 8
15 11 9 7 8 6 10 5 14 13 3 4
15 11 10 6 8 7 9 3 13 14 5 4
15 11 10 9 5 4 3 6 7 14 8 13
15 13 3 5 14 7 4 10 6 8 11 9
15 13 3 5 14 7 9 10 11 8 6 4
15 13 3 5 14 9 4 8 6 10 11 7
15 13 3 5 14 10 6 7 8 11 9 4
15 13 3 11 8 7 4 10 6 14 5 9
15 13 6 5 11 10 7 4 9 14 8 3
15 13 8 4 10 9 5 3 7 14 11 6
15 13 11 7 4 3 8 6 10 14 5 9
15 14 3 8 10 4 5 13 6 9 7 11
15 14 4 6 11 3 9 13 10 7 5 8
15 14 4 9 8 3 6 13 7 10 5 11
15 14 5 3 13 4 7 11 8 6 10 9
15 14 5 3 13 4 9 11 10 6 8 7
15 14 5 3 13 6 10 9 11 8 7 4
15 14 5 3 13 9 7 6 8 11 10 4
15 14 5 6 10 8 3 7 4 13 11 9
15 14 5 10 6 4 7 11 8 13 3 9
15 14 6 7 8 3 4 11 5 10 9 13
15 14 8 4 9 7 10 5 11 13 6 3
15 14 8 6 7 3 4 9 5 11 10 13
15 14 11 3 7 5 9 4 10 13 8 6
Here’s the code, btw:
#include <stdio.h>
#define NODES 12
int puzzle[NODES] = { 3,4,5,6,7,8,9,10,11,13,14,15 };
main() {
while(1) {
check_solved();
if( !shuffle() )
break;
}
}
int check_solved() {
int i;
if (
puzzle[0] + puzzle[2] + puzzle[5] + puzzle[7] == 35 &&
puzzle[0] + puzzle[3] + puzzle[6] + puzzle[10] == 35 &&
puzzle[7] + puzzle[8] + puzzle[9] + puzzle[10] == 35 &&
puzzle[1] + puzzle[2] + puzzle[3] + puzzle[4] == 35 &&
puzzle[1] + puzzle[5] + puzzle[8] + puzzle[11] == 35 &&
puzzle[4] + puzzle[6] + puzzle[9] + puzzle[11] == 35
) {
for( i=0; i<12; i++ )
printf( "%d ", puzzle* );
printf( "
" );
return 1;
}
return 0;
}
void swap(int i, int j) {
int temp;
temp = puzzle*;
puzzle* = puzzle[j];
puzzle[j] = temp;
}
int shuffle() {
int k,j,r,s;
k = NODES-2;
while ( puzzle[k] > puzzle[k+1]) k--;
if (k < 0) return(0);
else {
j = NODES-1;
while ( puzzle[k] > puzzle[j]) j--;
swap(j,k);
r = NODES-1; s = k+1;
while (r>s) {
swap(r,s);
r--; s++;
}
}
return(1);
}
Im not sure if your geting the point of the problem. I see all the possibilities, but what is the correct placement so the puzzle can be solved???
Well, discounting refelections and rotations there are 52 solutions, I think. Maybe any one of those solutions is acceptable…
Bill H. wrote
So, the first solution listed (3 4 5 15 11 14 8 13 7 6 9 10) goes:
3
4 5 15 11
14 8
13 7 6 9
10
What Bill H is trying to say ** Fugazi79**, is that those are ALL correct solutions, although a lot of them are reflections and rotations of others. Take your pick!
MonkeyMensch wrote
That is correct, Sir.
Here’s the list with reflections and rotations removed. (As you say, it’s 52 in length):
3 4 5 15 11 14 8 13 7 6 9 10
3 4 5 15 11 14 10 13 9 6 7 8
3 4 9 14 8 10 7 13 6 5 11 15
3 4 11 15 5 8 10 13 9 6 7 14
3 4 13 7 11 14 10 5 9 6 15 8
3 4 13 10 8 14 7 5 6 9 15 11
3 4 13 11 7 9 15 10 14 5 6 8
3 4 15 11 5 8 14 9 13 6 7 10
3 5 6 10 14 15 9 11 7 4 13 8
3 5 8 15 7 10 13 14 11 6 4 9
3 5 11 13 6 7 10 14 8 4 9 15
3 5 13 7 10 15 11 4 9 8 14 6
3 5 13 10 7 15 8 4 6 11 14 9
3 6 4 14 11 13 10 15 7 5 8 9
3 6 4 14 11 15 8 13 5 7 10 9
3 6 5 15 9 14 7 13 4 8 10 11
3 6 7 9 13 14 8 11 5 4 15 10
3 6 7 13 9 10 8 15 5 4 11 14
3 6 7 13 9 10 14 15 11 4 5 8
3 6 8 14 7 15 13 9 10 11 5 4
3 6 9 13 7 8 14 15 11 4 5 10
3 6 15 5 9 10 14 7 11 4 13 8
3 7 6 14 8 15 13 11 9 10 5 4
3 8 14 4 9 11 15 7 10 5 13 6
3 9 11 5 10 15 13 6 7 8 14 4
3 10 9 5 11 15 13 8 6 7 14 4
4 5 8 7 15 14 11 9 10 3 13 6
4 5 15 8 7 6 14 10 13 3 9 11
4 6 8 11 10 9 7 14 5 3 13 15
4 6 8 11 10 9 15 14 13 3 5 7
4 6 10 5 14 13 11 8 9 3 15 7
4 6 10 11 8 7 15 14 13 3 5 9
4 6 14 5 10 9 15 8 13 3 11 7
4 7 3 14 11 13 8 15 5 6 9 10
4 7 8 11 9 10 6 13 3 5 14 15
4 8 3 14 10 15 11 13 7 9 6 5
4 8 14 3 10 11 13 6 9 5 15 7
5 6 3 11 15 14 9 13 8 4 10 7
5 7 3 15 10 13 6 14 4 8 9 11
5 7 15 3 10 9 13 6 11 4 14 8
5 8 3 9 15 14 10 13 7 4 11 6
5 8 4 10 13 15 6 11 3 7 14 9
5 8 4 14 9 11 6 15 3 7 10 13
5 8 6 10 11 9 7 15 4 3 13 14
5 8 7 9 11 10 6 13 3 4 15 14
6 7 5 15 8 11 4 13 3 9 10 14
7 8 6 10 11 9 4 13 3 5 14 15
7 9 4 8 14 13 5 11 3 6 15 10
7 10 4 6 15 11 8 13 5 3 14 9
7 10 5 9 11 8 6 15 3 4 13 14
8 9 4 7 15 10 6 13 5 3 14 11
9 10 6 8 11 7 4 13 3 5 14 15
No shit! Your right. How could I not have accidentally stumbles on to one of those is all my efforts… lol, thanks guys. Got 25 more to go, ill be back im sure. 
Fugazi79 wrote
As was pointed out, this wasn’t a list of all possible combinations; it was a list of all working solutions. FYI, the total possible permutations is 79,001,599, of which only the 624 listed are correct. And of those, only 52 are “mathematically unique.”
Sorry, I meant 479,001,599.
So, the odds of “accidentally stumbling across one” is just better then one in a million.