Enigmas and ingenuity games

Grandfather's problem

Grandfather's problem
Grandfather problem

Here is one of those old problems that have passed from generation to generation without anyone having had the recklessness of questioning the accepted responses. However, recently, a young Boston fan received this relic from his grandfather and replied with such an unexpected solution that the old gentleman was speechless.

Many people have been asked very frequently to state the weight difference between six dozen dozen pounds of feathers and half dozen dozen pounds, and everyone answers without a moment of hesitation. "A pound is a pound worldwide," they say, "six dozen dozens give 864, and half a dozen dozens are 72, which makes a difference of 792 pounds".
However, if the question is formulated once again with all seriousness, and one grants enough attention, it will be discovered that it has never been correctly answered since the first time it was formulated in 1614.

Solution

To respond to this old riddle, we must take into account that gold is weighed according to the Troy system (in which a pound equals 12 ounces), while the feathers are weighed in Avo -Lupois units (where the pound is equivalent to 16 ounces ). In those cases the maximum "a pound is always a pound" is not valid.

Six dozen dozen pounds weigh 864 avoirdupois pounds, while 72 Troy gold pounds are equivalent only to 59 pounds, 3 ounces and 407.5 grains. As 864 pounds can be expressed as 863 pounds, 15 ounces and 437.5 grains, we have to subtract 59 pounds, 3 ounces and 407.5 grains to obtain 804 pounds, 12 ounces and 30 grains. That is our answer expressed in Avoirduis units.

People in general do not know the relationship between both systems. Some believe that the pound weighs the same in both, but in one system it is divided into 16 ounces and in the other in 12. Most people, however, believe that ounces are the same, but that the avoirdupois pound weighs 16 ounces and the pound Troy only 12. None of it is true. The relationship between both systems is based on the fact that an avoirdupois pound weighs 7.000 grains, while a Troy ounce weighs only 5.760 grains.