Let's look at groups of 3 digits that sum to zero (5 groups):
(0,5,-5), (0,1,-1), (0,-2,2), (7,-5,-2), (5,-1,-4)
0 appears in 3 groups; 7 appears in 1 group; 5 appears in 2 groups; 1 appears in 1 group; -1 appears in 2 groups; -4 appears in 1 group; -5 appears in 2 groups; -2 appears in 2 groups; 2 appears in 1 group.
Three numbers also appear with negative counterparts: (1,-1), (2,-2), (5,-5).
We have 5 intersecting regions:
Region A contains the numbers 7 -5 -2
Region B contains the numbers 5 -1 -4
Region C includes (overlaps) -1 from Region B, 0 and 1
Region D includes (overlaps) -2 from Region A and 0 from Region C and 2
Region E includes (overlaps) -5 from Region A, 5 from Region B and 0 from Region C
Each region contains numbers whose sum is zero. The singletons 7, 1, -4 and 2 lie outside the intersecting parts of their respective regions (A, C, B and D). 0 is part of overlapping Regions C, D and E and occupies the central position in the regions. The picture below shows 7 circular or elliptical shapes. The central circle containing 0 is enclosed by three ellipses but sits in between two other circles, the contents of which sum to zero, Region A being the right-hand circle and Region B the left. The contents of each ellipse also sum to zero. Region C is the ellipse leaning to the right, Region D the ellipse leaning to the left and Region E is the horizontal ellipse.
