Hungry Worm and Old Tree Riddle | Puzzles for Interview - Interview Preparation PDF Download

Introduction

A worm is very hungry and reaches an old tree. It starts eating the leaves in a particular sequence. On the first day, it eats one leaf. On the second day, it eats twice the number of leaves it ate on the first day, which is two leaves. On the third day, it eats twice the number of leaves it ate on the second day, which is four leaves. This continues for 30 days, with the worm eating double the number of leaves it ate on the previous day. On which day did the worm finish exactly half of the total number of leaves on the tree

Solution

To make the calculation easier, let's consider a shorter time frame of four days instead of 30. On the first day, the worm eats one leaf. On the second day, it eats two leaves (twice the number of leaves it ate on the first day). On the third day, it eats four leaves (twice the number of leaves it ate on the second day). On the fourth day, it eats eight leaves (twice the number of leaves it ate on the third day). All the leaves are finished on the fourth day, and the total number of leaves on the tree is 15 (1 + 2 + 4 + 8).
Half of the total number of leaves on the tree is 7.5 (15/2). At the end of day three, the worm can finish a total of seven leaves. Therefore, the worm finishes exactly half of the total number of leaves on the tree only on the last day, which is day four.

Conclusion

In the given riddle, where the time duration is 30 days, the worm finishes exactly half of the total number of leaves on Day 30, which is the last day.