A family has a mining claim. The claim actually belongs to the father, but the two brothers are now working it. The agreement is that they give their father a minimum of 10% (rounded up to the next full ounce) of each seasons take - and the two brothers split the remainder.
This year, they have collected 1.5 lbs of gold dust. They have a balance scale and a 5 ounce weight to work with.
What is the least amount of weighings that will be required to split the profits correctly?
Please explain your answer.
ok i think it would be 8 if they already knew they had 24 oz of dust, if they didn't then it's going to be a lot more.
the dad needs 3 oz for his 10% rounded up.
4 weighings with the 5oz weight makes them have 5 piles of gold, 5, 5, 5, 5, 4
now they put the 4 oz pile on one side of the scales and a 5 oz pile on the other then take gold from the 5oz side until they balance meaning that was 1 oz of gold they removed, they put that to one side for dad and repeat the process with another 2 piles of 5oz so they now have dad's 3 ozs of gold and 5 piles of gold 4, 4, 4, 4, 5.
so far that's 7 weighings and the last 1 is to split the 5oz pile 50/50.
now they each have 2 piles of 4 oz gold and a pile of 2.5oz gold.
just had a thought are we dealing with lbs and ozs or troy lbs and ozs? because there's only 12 troy ozs to a troy lb unlike the usual 16oz to 1lb.
just had a thought are we dealing with lbs and ozs or troy lbs and ozs? because there's only 12 troy ozs to a troy lb unlike the usual 16oz to 1lb.
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