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Interview prep / Brainteaser/Logic

Snaps needed to split a 6 by 8 chocolate bar

Question

A chocolate bar is a 6×86\times8 grid of squares. Each break takes one piece and snaps it along a straight line into two pieces. How many breaks are needed to separate it into 4848 single squares?

Short answer

4747. Every break raises the number of pieces by exactly one, so going from 11 piece to 4848 needs 4747 breaks regardless of the order.

Adapted from Zhou, A Practical Guide to Quantitative Finance Interviews, sec. 2.8 Math Induction, 'Chocolate bar problem', p.27; question and answer rewritten by SelfMadeQuant.com.

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