bonanova Posted June 5, 2008 Report Share Posted June 5, 2008 You just bought a rectangular bar of chocolate. It has been marked into pxq tiny squares. Since you are of generous nature, you want to share it with me. So you wish to break the bar into its individual constituent squares. At each step, you may pick up one piece and break it along any of its marked horizontal or vertical lines. What is the smallest number of steps that will accomplish this? Quote Link to comment Share on other sites More sharing options...
0 itachi-san Posted June 5, 2008 Report Share Posted June 5, 2008 You just bought a rectangular bar of chocolate. It has been marked into pxq tiny squares. Since you are of generous nature, you want to share it with me. So you wish to break the bar into its individual constituent squares. At each step, you may pick up one piece and break it along any of its marked horizontal or vertical lines. What is the smallest number of steps that will accomplish this? 1? no way right? i'm missing something i'm sure... but if p = 1, and q = 2 then half for me and half for you! Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted June 5, 2008 Author Report Share Posted June 5, 2008 1? no way right? i'm missing something i'm sure... but if p = 1, and q = 2 then half for me and half for you! Right. Sort of. You answered the question: what are the values of p and q for which a minimal number of steps are needed ... etc. The answer needs to be true for any values of p and q. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted June 5, 2008 Report Share Posted June 5, 2008 My answer is pq-1 breaks, but I don't have a proof for it right now. I'm going to sleep now, but maybe I'll have a proof poof into my head while I sleep. That or someone will probably beat me to it. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted June 5, 2008 Report Share Posted June 5, 2008 pxq - 1 As there will be number of (pxq) small pieces of chocoloate, and you can only pick up one at a time. However, when comes to the (pxq-1)th times, the pick up in fact break up the last 2 pieces apart, and that's it. right? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted June 5, 2008 Author Report Share Posted June 5, 2008 You both have it. woon has the proofyou start with 1 piece you end up with pq pieces. each step adds a piece. Quote Link to comment Share on other sites More sharing options...
Question
bonanova
You just bought a rectangular bar of chocolate.
It has been marked into pxq tiny squares.
Since you are of generous nature,
you want to share it with me.
So you wish to break the bar into its individual constituent squares.
At each step, you may pick up one piece and break it along any
of its marked horizontal or vertical lines.
What is the smallest number of steps that will accomplish this?
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