questions

The Puzzle: How many steps are required to break an m x n bar of chocolate into 1 x 1 pieces? You can break an existing piece of chocolate horizontally or vertically. You cannot break two or more pieces at once (so no cutting through stacks).

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The Solution . . .

You need mn – 1 steps. By breaking an existing piece horizontally or vertically, you merely increase the total number of pieces by one. You already have 1 piece, so need mn – 1 steps to get to mn pieces.