Challenging Brain Teaser for August 17: Test Your Puzzle Solving Skills!

Steps Required for Breaking a Chocolate Bar

Introduction

To determine how many steps are necessary for Dr. Johnson to break an m × n sized chocolate bar into 1 × 1 pieces, we can analyze the process mathematically.

Calculation of Steps

The number of steps required can be expressed as either of the following formulas:

1. (m – 1) + (n – 1) × m
2. (n – 1) + (m – 1) × n

Both formulas yield the same result:

– For the first formula:
– (m – 1) + (n – 1) × m
– = m – 1 + nm – m
– = nm – 1

– For the second formula:
– (n – 1) + (m – 1) × n
– = n – 1 + mn – n
– = mn – 1

Conclusion

In conclusion, Dr. Johnson requires a total of mn – 1 steps to break an m × n chocolate bar into individual 1 × 1 pieces.