Math Is Fun Forum

i try to repeat my explanation from my first post and being more clear.

list = 1,2,3,4,5

it is possible to combine only 1 with 5, and 2 with 4, symmetrically swapped with 3 as the center

the outcome should be:

1,2,3,4,5
1,4,3,2,5
2,1,3,5,4
2,5,3,1,4
5,2,3,4,1
5,4,3,2,1
4,1,3,5,2
4,5,3,1,2

(3 can also being left out, as it is the center and is not being picked / taken into account for the combinations)

trying to show you the relations by marking the numbers who are swapped together with either () or []:

(1),[2],3,[4],(5)
(1),[4],3,[2],(5)
[2],(1),3,(5),[4]
[2],(5),3,(1),[4]
(5),[2],3,[4],(1)
(5),[4],3,[2],(1)
[4],(1),3,(5),[2]
[4],(5),3,(1),[2]

or, to say it in different words, those 24 solutions / combinations of 1,2,4,5 (order important, repetition not allowed) are NOT VALID because 1,5 and 2,4 not symmetrical as a pair in relation to 3 (as explained above):

1,2,3,5,4
1,4,3,5,2
1,5,3,2,4
1,5,3,4,2
2,1,3,4,5
2,5,3,4,1
2,4,3,1,5
2,4,3,5,1
5,2,3,1,4
5,4,3,1,2
5,1,3,2,4
5,1,3,4,2
4,1,3,2,5
4,5,3,2,1
4,2,3,1,5
4,2,3,5,1