Caterpillar Climbing Problem

Pole height = 75 inches
Climbs up = 5 inches/day
Slides down = 4 inches/night

Net climb per day (after sliding): 5 - 4 = 1 inch

On the last day, caterpillar reaches the top without sliding back.

So, after n days, it reaches or passes 75 inches.

At the start of the n^th day, it has climbed:

(n - 1) × 1 = n - 1 inches

On the n^th day, it climbs 5 inches:

(n - 1) + 5 ≥ 75

Solving for n:

n - 1 + 5 ≥ 75
n + 4 ≥ 75
n ≥ 71

Answer: The caterpillar reaches the top on the 71^st day.