How many steps are required for Dr. Johnson to break an m × n sized bar of chocolate into 1 × 1 pieces?

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Answer: mn-1.

To break an m × n sized bar of chocolate into 1 × 1 pieces Dr. Johnson needs either ( m-1) +(n-1) x m steps or (n-1) + (m-1) x n steps.
( m-1) +(n-1) x m= m – 1 + nm – m = nm – 1
(n-1) + (m-1) x n = n – 1 + mn –n = mn – 1

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