The “Man Fell in Well” puzzle is a classic riddle that goes like this:
After falling into a well that is 30 meters deep, a man can climb up 4 meters during the day but slips back down 3 meters. What is the number of days required for him to climb out of the well?
Man Fell in Well Puzzle solution
To calculate the number of days required for the man to climb out of the well, we need to determine how many meters he will have to climb in total.
- Determine the man’s daily progress: He climbs up 4 meters but slips back down 3 meters, resulting in a net progress of 1 meter per day.
- Calculate the number of days required: The well is 30 meters deep, and the man’s net progress each day is 1 meter. Therefore, he will need to make 29 meters of progress to climb out of the well (30 meters depth – 1-meter progress made each day = 29 meters remaining). Since he makes 1 meter of progress per day, he will need 29 days to climb out of the well.
- Re-calculate the number of days required: However, we must consider that on the 27th day, the man will climb 4 meters, which will bring his total climb to 30 meters. Therefore, it will take 27 days for the man to climb out of the well.
- Determine the man’s maximum height: On the first day, the man can climb up to a maximum height of 4 meters. On the second day, he can climb up to a maximum height of 5 meters. On the Nth day, his maximum height will be N+3 meters.
- Find the value of N: To reach a height of 30 meters, N must be 27. Therefore, on the 27th day, the man will climb up to a height of 31 meters, which will allow him to escape from the well.