Brain Teaser: Solve Chocolate Bar Puzzle in Min Breaks

  • Context: High School 
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Discussion Overview

The discussion revolves around a puzzle involving a chocolate bar that is 6 blocks wide and 9 blocks long. Participants are exploring how to split the bar into individual blocks using the minimum number of breaks, while also considering a generalization for bars of width w and length m.

Discussion Character

  • Exploratory, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant suggests that the answer is 13 breaks, or w+m-2, indicating this as an upper limit.
  • Another participant agrees with the calculation of 13 breaks and asks for clarification on the formula w+m-2.
  • A further clarification is provided that to break a bar into 6 pieces, 5 breaks are needed, leading to the general formula of w-1 + m-1.
  • One participant expresses appreciation for the explanation of the formula.
  • Another participant introduces a different approach by questioning the thickness of the bar and suggesting breaking and stacking it before making additional breaks.

Areas of Agreement / Disagreement

Participants generally agree on the calculation of breaks needed but explore different methods and interpretations, indicating that multiple views remain on the optimal approach.

Contextual Notes

There are unresolved assumptions regarding the thickness of the chocolate bar and how it may affect the breaking process.

fernanroy
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A friend of mine is really pulling my chain. He said the answer to this was right in front of me. I doubt that! Does anyone have an idea on this?


"I have a bar of chocolate 6 blocks wide by 9 blocks long and I want to split it into its individual blocks making the smallest number of breaks that I can. The breaks that I am allowed to make start on one side and finish on a different side without visiting a third side.


How many breaks must I make?

Can you generalize your answer bard that are to w blocks wide and m blocks long?"
 
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Let's see. The obvious answer is 13, or w+m-2. I'm sure there's a shorter answer. That's the upper limit.
 
Thank You!

DaveC426913 said:
Let's see. The obvious answer is 13, or w+m-2. I'm sure there's a shorter answer. That's the upper limit.

Makes sense now that I look at it! Would you elaborate w+m-2?
 
fernanroy said:
Would you elaborate w+m-2?
To break something into 6 pieces, you to need to make 5 breaks.

So, specifically: 9-1 + 6-1, or generally: w-1 + m-1.
 
DaveC426913 said:
To break something into 6 pieces, you to need to make 5 breaks.

So, specifically: 9-1 + 6-1, or generally: w-1 + m-1.

YES! Thanks so much! I appreciate it!
 
Hmm, what about breaking it then stacking it and breaking it again? How thick is this bar?
 

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