Cut the Stick Puzzle

Solution for Dividing Pieces of Unit Length

Solution – Because we can only cut each area of the stick once at a given time, we must maximize the pieces after each cut. As a result, the initial cut will split the stick into two halves of the longest possible length. In the next cut, further cut both of the acquired portions into two longest parts each. Repeat this process till you have N unit parts.

Illustration: 

Let us suppose that N = 100 

1st Cut: (50) + (50) 

2nd Cut: (25) + (25) + (25) + (25) 

3rd Cut : (12) + (13) + (12) + (13) + (12) + (13) + (12) + (13) 

4th Cut : (6) + (6) + (6) + (7) + (6) + (6) + (6) + (7) + (6) + (6) + (6) + (7) + (6) + (6) + (6) + (7) 

5th Cut : (3) + (3) + (3) + (3) + (3) + (3) + (3) + (4) + (3) + (3) + (3) + (3) + (3) + (3) + (3) + (4) + (3) + (3) + (3) + (3) + (3) + (3) + (3) + (4) + (3) + (3) + (3) + (3) + (3) + (3) + (3) + (4) 

6th Cut: 28 portions of 1 unit, 36 portions of 2 units 

7th Cut: 100 portions of 1 unit

Through this method, the goal to split a stick into unit lengths pieces can be done.