ayw wrote:I wonder how many different solutions there are
Okay, I wrecked my mind over that one for the last couple of hours...
there are at least 5solutions (including ayw's and googleearth's ones)
original circle (stolen from ayw ;-) )sockets (I will refer to it as the "original circle")
All of the following is about the plugs, the sockets remain unchanged!
1 is always were it originally was, starting from there clockwise:
[spoiler]a) 1,7,6,5,4,3,2 (googleearth)
b) 1,5,2,6,3,7,4 (ayw)
Here a lot of little mathematical curiosities I noticed while thinking about whether there are more solutions than these... not really significant but maybe interesting...
[spoiler]When writing them in circles (I couldn't be bothered doing that here) b) - c) and d) - e) are mirror images of one another. The mirror image of a) would be the "original circle". When adding up the number opposite of one another (with 1 having no corresponding number) they will always add up to 9.
When writing down how far each number was shifted from the "original circle" (1 always being shifted by 7 or 0), you can see that all of these are different possibilities (not just different labels). (All numbers from 1-7 being used is another way of saying no matter how you rotate the circle one of the plugs will always match the socket)
A) 7,5,3,1,6,4,2 (1 was shifted by 7, 2 was shifted by 5, 3 was shifted by 3...) -clockwise of course) - = 1,6,4,2,7,5,3,1 = e (same sequence)
B) 7,1,2,3,4,5,6 - same sequence as the original circle
C) 7,4,1,5,2,6,3 - same sequence as b
D) 7,3,6,2,5,1,4 - same sequence as c
E) 7,2,4,6,1,3,5 - same sequence as d
When writing these sequences in a circle, with 7 always being at the top, the numbers which are oppsite of one another will always add up
to 7. Here (written in a circle with 7 being on top) A) - E) and C) - D) are mirror images!
All of this is totally unsignificant to the answer but since there seem to be so many mathematical similarities and realtions between these 5 solutions I assume that these are the only ones-but I'm not sure
Few.. all of this took me about 2 and a half hours and 4pages of notes in 3 different colors... but at least the downloads for the two new DC episodes have finished now so I'll go and watch those
"It is one of those instances where the reasoner can produce an effect which seems remarkable to his neighbor, because the latter has missed the one little point which is the basis of the deduction."