The Farmer,
His Daughter And Her Suitor ...
And
The  Apple Problem

A young man asked the farmer for his daughter's hand in marriage.  Wanting to make sure the fellow had some wits about him the farmer posed this challenge to the young man:  "If you can go to the apple orchard and pick enough apples so that on the way back to the house you leave one half of the apples you picked plus one half an apple at each of the three gates you pass through and when you return to the house you have one single apple remaining for may daughter you may have her hand in marriage.  However if you cut any of the apples then you may not marry her".

The young man was deep in thought as he walked slowly down to the orchard.  He at first thought that this was impossible, how could one leave one half an apple without cutting it.  As he paused by the last gate he thought: "If I have one apple remaining when I return to the house how many would have at this gate?" 

He knew immediately that two apples would not do the trick because one half of two plus one half was one and a half and cutting an apple was against the rules.  Then he considered the number three:  One half of three was one and a half the plus one half was the number two and in the case that number be removed from three left one, the precise number required on returning to the house and nary an apple be cut into two!

The young man immediately realized that this sort of argument would work for an arbitrary number of apples that when that number of apples divided in half left over one.  This lead him to consider the number seven at the next to last gate, which when the half plus a half method be applied yielded three to carry forward to the last gate, which was the precise number required to yield one single apple at the end.

It was very short work for the young man to come up with the number fifteen for the original amount since the half plus one half method applied to this yielded seven and when applied again yielded three and when applied the third time yielded one, the required number of apples to complete with.

So after picking the fifteen apples and leaving the required number at each gate the young man completed the task set out and married the farmer's daughter and they lived happily ever after.
 

This Page Last Update Saturday, March 04, 2006 17:00:38 -0500