Answer:
There are a few ways to do this. One is
Here's a good way to approach this problem. Pick a circle, and
look at the four squares on that circle. Now look at the triangular
pattern formed by the six squares, and see which two the circle does
not go through. You should see that a given circle goes through
all the squares except one corner of the triangle and the middle of the
opposite side.
For example, the circle that goes through 24, 12, 6, and 18
"misses" 30 and 0 -- 30 is on the corner of the triangular
pattern, and 0 is in the center of the opposite side. Since
0+6+12+18+24+30=90, then the two numbers missed by the circle have
to add up to 30 so that the other four add up to 60.
The three corner-side pairs, then, have to be
0,30;
6,24; and
12,18.
It really doesn't matter how these are arranged on the diagram, as long
as one of each pair goes on a corner of the triangular pattern, and the
other goes in the opposite side.
