Breaking a chocolate bar
A chocolate bar is a grid of 48 squares. You want to break it into the 48 single squares. Each break takes one piece and splits it along a straight grid line into two pieces; pieces cannot be stacked.
What is the minimum number of breaks?
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
How does one break change the number of pieces?
You start with 1 piece and end with 48.
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s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. Every break turns one piece into two, so it increases the number of pieces by exactly one, whatever piece you break and however you break it.
Step 1. You start with 1 piece and need 48.
Step 2. Each break adds exactly one piece, so exactly breaks are needed.
So the answer is 47, and every strategy uses exactly that many: there is nothing to optimise.
The same idea. A knockout tournament with players needs matches, since every match eliminates exactly one player.