Mid-Week Recreation – The Weighing Stone

Hello everyone,

So while I am busy writing a Skyrim love letter post, a Symbiosis post (because that ability requires one almost entirely to itself), and battling a recent medical diagnosis, I’d like to give you something interesting to think about. A math riddle!

I know some of you were told there would be no math but…well if you’re reading my blog you know that I have a penchant for recreational math. As an engineer I generally deal with fairly concrete equations and guidelines so abstract mathematical analysis (which I did once upon a time) has long since left my brain. I will never compete with the likes of those that do the elitist jerks theorycrafting. If you’re comfortably on my level then hopefully you’ll appreciate this fairly straight forward puzzle! If you do come up with an answer please feel free to throw it in the comments but do so at your own risk as others may or may not drop one there. Do not leave explanations behind your answer as I’d like others who submit answers to not know if yours is right or wrong.

 

STONE RIDDLE

A long time ago there was a farmer who grew wheat to sell at the market. In order to bundle up his grain he would use a rather heavy-duty balance scale to check it against a stone that weighed exactly 40 lbs. Once a 40 lbs. Bushel was weighed it was strapped and thrown on the cart to bring to market.

One day the farmer’s neighbor came over and explained that he had broken his measuring stone and was in a dire situation getting his produce packaged up for the market. The farmer told his neighbor that he could use his 40 lb. stone, the only condition being that he had to take perfect care of it and return it safely. He was reassured this would be the case and off the stone went.

After a few days had gone by the neighbor returned on his wagon however the 40 lb. stone was not on it and intact. Instead the farmer saw four different size pieces of stone. The neighbor sheepishly admitted that the stone had slipped off of his scale and broke into four pieces. It turns out that each piece’s weight was a whole number, and once the farmer was told exactly how much each stone piece weighed he was no longer upset. It turns out that through clever manipulation the four pieces of stone could be used to measure any whole number increment of wheat from 1 to 40 pounds.

Goal:

If each of the four pieces’ weight is a whole number, all four of them add up to 40 pounds, and they can be used to weight any weight between 1 to 40 pounds how much does each stone weigh? The scale the farmer uses is a traditional balance beam scale with room to place items on either side. When wheat is being measured all wheat goes on the same side of the scale.

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