We want to find the heaviest and the second heaviest gem out of 32
having distinct weights and similar shape.
Only simple balance scale is available.
Specify the method to get the correct result within a minimal number of weighing.
Place the 32 gemstones into a single elimination bracket. This will take 31 weighings to find the heaviest gemstone. The second heaviest must be one of the five gemstones which lost to the heaviest gemstone. Then four more weighings are needed to find the second heaviest gemstone. This algorithm will always use 31+4 = 35 weighings to find both of the two heaviest gemstones.