A frog falls into a 20-meter-deep well. Every day, it climbs up 2 meters and falls back down 1 meter. How many days will it take for the frog to climb out of the well?
Each day, the frog makes a net gain of 1 meter (climbs 2 meters, falls back 1 meter).
After 17 days, the frog would have made a net gain of 17 meters (1 meter per day).
On the 18th day, the frog climbs 2 meters, reaching 19 meters, and then falls back 1 meter, ending up at 18 meters.
On the 19th day, the frog climbs 2 meters, reaching the top of the well at 20 meters, and escapes without falling back.
Therefore, it will take the frog 19 days to climb out of the well.
Here are the similar riddles along with their solutions:
- The Escaping Snail: A snail is at the bottom of a 30-foot well. Every day, it climbs up 3 feet and slides back down 2 feet. How many days will it take for the snail to escape the well?Solution:
- Each day, the snail makes a net gain of 1 foot (3 feet up – 2 feet down).
- To reach the top of the 30-foot well, the snail will make a net gain of 27 feet (since on the last day it won’t slide back).
- After 27 days, the snail will have climbed 27 feet.
- On the 28th day, the snail climbs 3 feet, reaching the top of the well at 30 feet and escapes without sliding back.
- The Leaping Frog: A frog is at the bottom of a 15-meter pit. Each day, it jumps up 3 meters but slips back 2 meters. How many days will it take for the frog to get out of the pit?Solution:
- Each day, the frog makes a net gain of 1 meter (3 meters up – 2 meters down).
- To reach the top of the 15-meter pit, the frog will make a net gain of 12 meters (since on the last day it won’t slip back).
- After 12 days, the frog will have climbed 12 meters.
- On the 13th day, the frog jumps 3 meters, reaching the top of the pit at 15 meters and escapes without slipping back.
- The Climbing Ant: An ant is at the bottom of a 10-foot deep well. Each day, it climbs up 2 feet but slides back down 1 foot. How many days will it take for the ant to reach the top of the well?Solution:
- Each day, the ant makes a net gain of 1 foot (2 feet up – 1 foot down).
- To reach the top of the 10-foot well, the ant will make a net gain of 9 feet (since on the last day it won’t slide back).
- After 8 days, the ant will have climbed 8 feet.
- On the 9th day, the ant climbs 2 feet, reaching the top of the well at 10 feet and escapes without sliding back.
- The Climbing Worm: A worm is in a 12-foot deep hole. Each day, it crawls up 4 feet but slips back 3 feet. How many days will it take for the worm to climb out of the hole?Solution:
- Each day, the worm makes a net gain of 1 foot (4 feet up – 3 feet down).
- To reach the top of the 12-foot hole, the worm will make a net gain of 8 feet (since on the last day it won’t slip back).
- After 8 days, the worm will have climbed 8 feet.
- On the 9th day, the worm crawls 4 feet, reaching the top of the hole at 12 feet and escapes without slipping back.
Brain Teaser Questions 