You’re handed a sweet but tricky problem:

A chocolate bar is made of 6 rows and 8 columns of small \(1 \times 1\) squares — that’s 48 total pieces.
You want to split it into all individual squares.

Each break splits one piece (which may be a rectangle) into two smaller rectangles along grid lines.

Question: How many total breaks are required?

Step 1: Understand the Process

Each break increases the number of pieces by 1.

  • Start: 1 large bar
  • End: 48 individual pieces

So, every time you break one piece into two, the total number of pieces increases by 1.

Step 2: Apply the Principle

To go from 1 piece → 48 pieces, you need:

\[ 48 - 1 = 47 \text{ breaks} \]

This logic is independent of how you make the breaks—whether you go row by row, column by column, or randomly.

Each break contributes exactly one new piece.

Bonus Interview Trick: What If You Can Stack?

In quantitative interviews, a common follow-up is: “What if you are allowed to stack the pieces on top of each other and cut through the stack simultaneously?”

If you stack the pieces, each cut can theoretically double the total number of independent blocks you have. Therefore, the minimum number of cuts needed to reach 48 independent pieces is determined by the base-2 logarithm:

\[ 2^k \ge 48 \implies k = 6 \text{ cuts} \]

With stacking allowed, the answer drops from 47 down to 6!

Final Answer

47 breaks are always required to split a chocolate bar into 48 individual squares—no matter the strategy.

Reference