Clock puzzle

So on an ordinary 12 hour clock, draw 2 lines between any set of numbers, from outside to inside, that is, intersecting a circle surrounding the numbers, say a line from the space between 7 and 8 and continuing to the space between 3 and 4, that kind of thing.

If the lines don't intersect, you have 3 spaces, if they intersect you have 4 spaces defined.

The puzzle is to place the lines in such a way that the addition of the resultant numbers are all equal.

Originally posted by sonhouse
So on an ordinary 12 hour clock, draw 2 lines between any set of numbers, from outside to inside, that is, intersecting a circle surrounding the numbers, say a line from the space between 7 and 8 and continuing to the space between 3 and 4, that kind of thing.

If the lines don't intersect, you have 3 spaces, if they intersect you have 4 spaces defined. ...[text shortened]... le is to place the lines in such a way that the addition of the resultant numbers are all equal.

Since the sum of 1 to 12 is 78 and 78/3=26:

One field with 11,12,1,2
one field with 10,9,3,4
and 5,6,7,8

Originally posted by Ponderable
Since the sum of 1 to 12 is 78 and 78/3=26:

One field with 11,12,1,2
one field with 10,9,3,4
and 5,6,7,8

Bingo! Tip o the hat to ye! Yep, you could see clearly it had to be a three partition, 4 would been 19.5 X4 =78. So the lines could never intersect leaving only a triple partition.

So.. slicing a dot in half so that 1 would be .5 on both halves would be uncool? I wonder if such a solution would exist..