This solution was sent in by someone who only gave us their initial "S":

1and 8 have only 2 and 7 next to them so I put them in the middle then I put 2 and 7 in the furthest away from their consecutive numbers. Then the next 2; 3 and 6 next to the numbers jut 2 away from them. the other 2 are easy 5 at the bottem and 4 at the top.

And here is an interesting way of approaching the problem sent in by Timothy. Notice that Timothy has turned the diagram on its side:

The solution to the above is:

                      6     4
 

 
                  2     8     1     7
 

 
                        5     3
 
   
 

             

How I did this was I numbered the circles 1 to 8 like this :

                      4     3
 

 
                  5     8     7     2
 

 
                        6     1
 
    
 

             

The way that I learned to do this puzzle is for a start put the numbers 1 and 8 in the middle circles. I then started by looking at the circle numbers that were not together, then I started making lists of the circle numbers that were not together, then I made larger lists of the circle numbers, and then each list taught me another step until I had all the pieces of information I needed. then I made the correct list which was:

7,5,1,3,6,4,2,8
1,2,3,4,5,6,7,8

The top row are the circle numbers, and the bottom row are the numbers which go into the circles.