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Breaking a Chocolate Bar (illustration)
FILE No.124Unsolved

Breaking a Chocolate Bar

Difficulty ★★☆about 5 minLogic PuzzleInvariantsHow to count
What is the fewest breaks needed to separate a 6×8 chocolate bar into single pieces?

Case Record

There is a chocolate bar of 6 pieces by 8 pieces. With each snap you break one chunk into two along a straight line. (You may not stack pieces and break them together.)

Your question

What is the fewest number of breaks needed to separate it into single pieces?

Case Files

Diagram

A 6 × 8 chocolate barEach break splits one piece in two along a straight line (no stacking).What is the fewest breaks needed to get 48 single pieces?
Diagram

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

How many more chunks do you get from one break?

Open hint 2

How many chunks are there at the end?

Open hint 3

Does the order of breaking matter?

Solve It

Your question

What is the fewest number of breaks needed to separate it into single pieces?

Choose the answer closest to the truth.

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The Truth

47

The answer is "47."

Each break increases the number of chunks by one. You start with 1 chunk and end with 48. So you need 47 breaks.

The number of breaks is the same in any order.

Each break adds exactly one pieceBreaksPieces011223……4748We end with 48 pieces, so 47 breaks, in any order.
Diagram of the solution

Key Points

  • Each break adds one chunk
  • Count the difference between start and end
  • No clever way of breaking is needed

Why people get fooled

Because you try to be clever about breaking along rows and columns.

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