Challenging Brain Teaser for September 2: Test Your Wits Today!

Steps Required to Break a Chocolate Bar

Introduction

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

Calculation of Steps

The total number of steps required can be expressed in two equivalent ways:

1. **First Method**:
– Steps = (m – 1) + (n – 1) × m
– Simplifying:
– = m – 1 + nm – m
– = nm – 1

2. **Second Method**:
– Steps = (n – 1) + (m – 1) × n
– Simplifying:
– = n – 1 + mn – n
– = mn – 1

Conclusion

In both methods, the outcome is the same. Therefore, the total number of steps required for Dr. Johnson to break the chocolate bar into 1 × 1 pieces is given by the formula: **mn – 1**.