A caterpillar crawls up a pole of 75 inches high, starting from the ground. Each day, it crawls up 5 inches and each night it slides down 4 inches. When will it reach the top of the pole?
This is a classic logical puzzle where the key is to realize that on the day the caterpillar reaches the top, it does not slide back down at night.
First, let's determine the caterpillar's net progress over a full 24-hour cycle (one day and one night).
The caterpillar reaches the top of the 75-inch pole during its daytime climb of 5 inches. We need to find out how many days it takes for the caterpillar to be in a position where it can reach the top in that one final climb.
The starting height for the final day's climb must be at least:
75 inches (total height) - 5 inches (day's climb) = 70 inches.
Since the caterpillar makes a net progress of 1 inch per day, it will take exactly 70 days (and 70 nights) to reach a height of 70 inches.
At the end of the 70th night, the caterpillar is at a height of 70 inches. On the morning of the 71st day, it begins to climb.
It will climb the remaining 5 inches and reach the top of the pole during the 71st day.
The caterpillar will reach the top of the pole on the 71st day.
Reinforce your conceptual grasp with related questions from NIMCET 2018:
Let S be the set of integers x such that
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