A frog is at the bottom of a 30-foot well. Each day, the frog climbs up 3 feet, but every night, it slips back 2 feet. The question is: how many days will it take the frog to escape the well?

Objective:
Determine the number of days it will take for the frog to climb out of the well.

Solution

To solve this puzzle, we need to account for the net progress the frog makes each day and consider what happens on the final day when the frog escapes the well.

Step-by-Step Solution for the Frog and the Well Puzzle:

Step 1: Calculate the Net Progress per Day

Each day, the frog climbs up 3 feet but slips back 2 feet at night. Therefore, the net progress the frog makes each day is:

• Net progress per day = 3 feet (climbed) - 2 feet (slipped back) = 1 foot per day

Step 2: Determine the Frog’s Position Just Before Escaping

The frog needs to reach the top of the 30-foot well. However, the key point is that on the final day, the frog will climb 3 feet without slipping back, as it will escape the well before slipping occurs.

• After 27 days, the frog would have climbed a total of 27 feet (since it makes 1 foot of net progress per day).

Step 3: Calculate the Final Day’s Climb

On the 28th day, the frog starts at 27 feet. It climbs 3 feet during the day, reaching the top of the well:

• 27 feet + 3 feet = 30 feet

Since the frog escapes the well on the 28th day, it does not slip back this time.

Step 4: Conclusion

The frog successfully escapes the well on the 28th day.

Final Answer

The frog will take 28 days to escape the 30-foot well.