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Cut a gold bar into seven pieces with two cuts.

This is how the problem was phrased when I found it on the web.

You’ve got someone working for you for seven days and a gold bar to pay them. The gold bar is segmented into seven connected pieces. You must give them a piece of gold at the end of every day. If you are only allowed to make two breaks in the gold bar, how do you pay your worker?

3 replies on “Cut a gold bar into seven pieces with two cuts.”

I think they mean cut and not break.. if they do then the solution is to have a wavy first cut through the bar in a “wavy pattern”. Then have the second cut chop through the wavy section – in essence the next single cut cuts the peaks off the wavy section. This way the second cut makes multiple pieces from a single cut.

To get seven pieces framed by the problem use a sine pattern with 2.5 periods. That cuts into 5 peak / trough pieces and two larger edge pieces.

two_cuts_seven_pieces

Grrr… I think I am being dumb about this. The fact that the problem explicitly says the bar is “segmented into seven connected pieces” makes me think – I am missing something and that I am missing something. Then again – the way people “re-word” problems when the rip them off someone could have injected this error when copying the problem to post on the web.

Yeah, Konrad made it obvious what I was missing in this problem. He re-worded it as:

> You and your crazy friend are working alone together on a space station. Your
> friend insists on being paid exactly $1000 at the end of each single day, but when
> you are in transit to the space station you realize that there are only three
> checks left in your checkbook, while you will be working with this weirdo for
> seven days. If there ever comes a day when you don’t give him a check, Something
> Bad Will Happen. What amount should you write on each of the three checks to
> ensure that at the end of each day your friend can hold exactly his cumulative
> salary in checks?

Which makes the answer obvious. Split the bar into a piece one segment in size, two segments in size, and four segments in size. Which requires the two breaks we are able to make in the bar. This makes the answer:

day one – give them the size onepiece of gold
day two – swap him the size two piece of gold for the size two piece.
day three – give him the size one piece of gold. day four – swap him his gold for the size four piece
day five – give him the size one piece
day six – swap him the size one piece for the size two piece.
day seven – give them all the gold.

Ugh, so simple once you see what they were asking for.

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