Well this puzzle is interesting. you have to think such that with the solution everybody is happy and no body has suffered a loss.
Let's see the problem first.
we have 17 horses to be divided among three sons with the ratio as given.
1st son -- half of the horses (17/2)=8.5
2nd son -- one third of horses (17/3)=5.66
3rd son -- one ninth of horses (17/9)=1.88
Now all the results are in fraction so the horses cannot be distributed like this. What will the traveling mathematician do to solve it.
It's simple.He will add his horse to the group of horses. So in total we have 18 horses now. Now let's see the scenario again.
1st son -- half of the horses (18/2)=9
2nd son -- one third of horses (18/3)=6
3rd son -- one ninth of horses (18/9)=2
So in total 17 horses will get distributed among the three sons and the traveling mathematician will take his horse and leave.
Let's see the problem first.
we have 17 horses to be divided among three sons with the ratio as given.
1st son -- half of the horses (17/2)=8.5
2nd son -- one third of horses (17/3)=5.66
3rd son -- one ninth of horses (17/9)=1.88
Now all the results are in fraction so the horses cannot be distributed like this. What will the traveling mathematician do to solve it.
It's simple.He will add his horse to the group of horses. So in total we have 18 horses now. Now let's see the scenario again.
1st son -- half of the horses (18/2)=9
2nd son -- one third of horses (18/3)=6
3rd son -- one ninth of horses (18/9)=2
So in total 17 horses will get distributed among the three sons and the traveling mathematician will take his horse and leave.
4 comments:
The difficulty is that the original problem is not solved by the 18th horse. It seems to be, but only if you forget part of the problem.
Forget the 17 horses for a moment. Just think about the fractions.
1 – (1/2 + 1/3 + 1/9) = 1/18
So there’s a one eighteenth share of the horses that is not given to any of the sons. That is either given to a fourth party not mentioned in the problem or goes to the state because it’s unaccounted for in the will.
When they borrow the 18th horse, they don’t just add that one in, they also add in the fourth party’s share. The 18th horse is irrelevant. They solve the problem through theft. Everyone ignores this bit.
Though I’d add a question six: Who got the farm? (He was a farmer, remember?) Even if the farm was rented, there would still be farming equipment and machinery. And there would be animals and/or crops too.
1st son -- half of the horses (17/2)=8.5
2nd son -- one third of horses (17/3)=5.66
3rd son -- one ninth of horses (17/9)=1.88
this adds up to 16.05 horses. Still impossible to split in these fractions!
The old farmer was a poor mathematician. One half plus one third plus one ninth does not add up to a whole, it's one-eighteenth short. Perhaps there was a secret fourth son with the miller's wife down the lane?
An easier way to resolve the division without borrowing an extra horse is simply to round all the numbers down. The oldest son gets 8 horses, the middle son gets 5 and the youngest gets 1. There are then three horses left over, the sons take one each and since each one now has slightly more than his share, they are all happy.
Except for that secret fourth son, who gets nothing.
The farmer was trying to teach his illiterate sons some math because they skipped school to go fishing. Unfortunately he was drinking at the time he made the will and he tossed fractions out willy-nilly. But it's not a problem because the neighbor is quietly taking a head or two of livestock home with him every time he visits.
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