Princess Catharina's Gold Rings Investigating 5 and 6 in the top drawer

Twelve (12) rings. Their weights are: 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17 and 40 grams.

If we put 5 and 6 in the top drawer, we only need one more ring to fill it.
Try every other number one at a time to find which ones work.

TOP (3) 5 ... 6 ... 7 Total = 18 MIDDLE (4) Not 4 left that add to 36. Total = 36 BOTTOM (5) __ ... __ ... __ ... __ ... __ Total = Can't do it.

TOP (3) 5 ... 6 ... 8 Total = 19 MIDDLE (4) Not 4 left that add to 38. Total = 38 BOTTOM (5) __ ... __ ... __ ... __ ... __ Total = Can't do it.

TOP (3) 5 ... 6 ... 9 Total = 20 MIDDLE (4) 7 ... 8 ... 10 ... 15 Total = 40 BOTTOM (5) 11 ... 14 ... 16 ... 17 ... 40 Total = 98

TOP (3) 5 ... 6 ... 9 Total = 20 MIDDLE (4) 7 ... 8 ... 11 ... 14 Total = 40 BOTTOM (5) 10 ... 15 ... 16 ... 17 ... 40 Total = 98

TOP (3) 5 ... 6 ... 10 Total = 21 MIDDLE (4) 7 ... 8 ... 11 ... 16 Total = 42 BOTTOM (5) 9 ... 14 ... 15 ... 17 ... 40 Total = 95

TOP (3) 5 ... 6 ... 10 Total = 21 MIDDLE (4) 7 ... 9 ... 11 ... 15 Total = 42 BOTTOM (5) 8 ... 14 ... 16 ... 17 ... 40 Total = 95

TOP (3) 5 ... 6 ... 10 Total = 21 MIDDLE (4) 8 ... 9 ... 11 ... 14 Total = 42 BOTTOM (5) 7 ... 15 ... 16 ... 17 ... 40 Total = 95

TOP (3) 5 ... 6 ... 11 Total = 22 MIDDLE (4) __ ... __ ... __ ... __ Total = 44 BOTTOM (5) __ ... __ ... __ ... __ ... __ Total = __

HERE

TOP (3) 5 ... 6 ... 14 Total = 25 MIDDLE (4) 7 ... 10 ... __ ... __ Total = 50 BOTTOM (5) __ ... __ ... __ ... __ ... __ Total = __

TOP (3) 5 ... 6 ... 14 Total = 25 MIDDLE (4) 7 ... __ ... 15 ... __ Total = 50 BOTTOM (5) __ ... __ ... __ ... __ ... __ Total = __

TOP (3) 5 ... 6 ... 14 Total = 25 MIDDLE (4) 8 ... __ ... __ ... __ Total = 50 BOTTOM (5) __ ... __ ... __ ... __ ... __ Total = __

TOP (3) 5 ... 6 ... 14 Total = 25 MIDDLE (4) 9 ... __ ... __ ... __ Total = 50 BOTTOM (5) __ ... __ ... __ ... __ ... __ Total = __

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