Breaking a chocolate bar

Task number: 3326

let’s have a chocolate bar with \(m\times n\) squares. Determine how many times you must break some piece of chocolate into two smaller pieces until you obtain \(mn\) individual squares.

Find a way to break the bar with as few breaks as possible.

  • Solution

    Let \( f(m,n) \) be the number of table breaks with dimensions \( m \times n \). The following identities follow from the assignment:


    These have the solution \( f (m, n) = mn-1 \).

  • Answer

    The breaking procedure is irrelevant, it will always be necessary to break \( mn-1 \) times.

Difficulty level: Moderate task
Reasoning task
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