Wednesday, December 23, 2009

The Housekeeper and the Gold Brick

A woman in the country of Florin hired a skillful, but untrustworthy nomad to feed her animals and harvest her crops once a day, for 7 days.  Due to inflation, Florinese currency had become worthless and she agreed to pay the man in gold at the rate of 1 gold piece per day.  She did not trust him enough to pay him up front, and he did not trust her enough to receive payment after all services had been rendered.  So he would have to have 1 piece at the end of the first day, 2 pieces at the end of the second day, and so on until he had all 7 pieces at the end of the seventh day.  

The woman only had one solid gold brick, divided with notches into 7 sections like a Kit-Kat bar.  Each section was worth one gold piece.  The trouble is, she could only have it cut along the notches, and only twice (don't ask why - I don't know).  How could she cut this 7-piece brick along only two of the notches, but still be able to pay the nomad 1 piece per day?

She can cut the brick into a 1-piece section, a 2-piece section, and a 4-piece section.  On day 1 she gives the nomad 1-piece.  On day 2, she takes back the 1-piece and gives him the 2-piece, so he walks away with 2 pieces total.  On day 3 she gives the 1-piece - now he has 3 pieces.  On day 4, she takes back the 1 and 2 and gives him the 4.  On day 5, she gives the 1 in addition to his 4, so he has 5.  On day 6 she takes back the 1 and gives the 2.  Finally on day 7, she gives him all of the gold. 

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