A Smart Interview Question From The Campus Of Kharagpur

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A Smart Interview Question From The Campus Of Kharagpur

image containing math problem statement

A smart problem asked during a campus interview at IIT Kharagpur. Requires no more than thinking, not even a pen and paper.

Problem contributed by debosmita1729

Let $k$ denote the number of breaks performed. Let $P_k$ denote the total number of separate chocolate pieces existing after the $k$-th break.

Initial State ($k=0$): We begin the whole $6 \times 8$ bar.

$P_0 = 1$
Target State: We wish to separate the bar into individual unit squares. The total number of squares is:

Thus, the target is to reach a state where $P_{k} = 48$.

When you break a rectangular piece, no matter which piece you break or along which line, the result is always one additional piece to the existing count of pieces.

In the final state we will have $48$ pieces and the initial state has $1$ piece.

Therefore you need exactly $48 - 1 = 47$ breaks to make $48$ pieces.