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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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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!

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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.

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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.

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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?

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