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A possible indication of the difficuly of a s puzzle is the number of circles - the number of given sumthing areas. The larger this difference is the less direct dependence there is between the different values of the circles, and the dependence must now come from the fact that sumthing puzzles do not allow any of the circle values to repeat, and the integer nature of the circle values as well as their limited range.

Thus if we define the rank of a sum-thing puzzle as the difference between the number of circles and the number of given sum-thing areas (do not count empties) What is the largest possible rank of a sumthing puzzle. On puzzle picnic there must be a definite answer since the rank is less than 24 (25 cirlcles 1 Area), this is of course impossible because the order of the circle values would not be uniquely defined. My current best (Not verified yet) is 9 (20 circles, 11 sumthing areas).

I think I've improved my best to 15.

I have an unverified puzzle in the vestibule with 25 circles and 10 sum thing areas.

I've been able to lower the amount of sum thing areas to 8 in a 25 circle puzzle (Still in the vestibule). Unlike before I worked hard to try to get 7 areas with no success till now.

After more work I'm down to 7 areas in a 25 circle puzzle. I'll try to extend to 6????