The Frog and the Well Puzzle is one of the most well-known logic and arithmetic puzzles in the world. It appears simple at first glance, but the catch lies in understanding the net progress and the behavior on the final day. This puzzle is popular in reasoning tests, aptitude exams, and interviews because it challenges both logical and mathematical thinking in a single setup.
The problem usually goes like this: a frog is stuck at the bottom of a 30-foot well. Every day, it climbs up a few feet, but during the night, it slips back down. The goal is to find out how many days it will take for the frog to finally escape the well.
Frog and Well Puzzle
Objective
Determine how many days it will take for the frog to climb out of the 30-foot well.
The puzzle teaches persistence, logical calculation, and attention to detail. While the frog’s daily progress seems small, consistency and timing are what make the difference. The trick is realizing that the frog doesn’t slip back on the day it escapes.
Puzzle Setup and Rules
Let’s restate the puzzle clearly before solving:
- The frog is at the bottom of a 30-foot well.
- Each day, it climbs up 3 feet.
- Each night, it slips back 2 feet.
- The process repeats daily until the frog escapes.
The question:
How many days will it take for the frog to escape the well completely?
At first, one might think 30 feet divided by the net gain of 1 foot per day means 30 days. But that misses the crucial detail about what happens on the last day when the frog finally reaches the top.
Step-by-Step Solution for the Frog and the Well Puzzle
The solution requires simple reasoning and a bit of careful counting. Let’s go step by step.
Step 1: Calculate the Net Progress per Day
Each day:
- The frog climbs 3 feet during the day.
- It slips back 2 feet at night.
So, the net progress per day is:
Net progress = 3 - 2 = 1 foot per day.
That means after each full day (including slipping at night), the frog is 1 foot higher than it was the previous morning.
Step 2: Determine the Frog’s Position Before the Final Climb
The frog needs to reach the top of the 30-foot well. However, it won’t slip back on the day it escapes because it will reach the top before nightfall.
So, we need to find when the frog gets to a height from which it can climb out in one final move.
After 27 days, the frog will have climbed:
27 feet (since it gains 1 foot net progress each day).
On the morning of the 28th day, the frog starts at 27 feet.
Step 3: Calculate the Final Day’s Climb
On the 28th day, the frog climbs up 3 feet:
27 + 3 = 30 feet.
At this point, the frog has reached the top of the well and escapes.
Since it’s already out, it does not slip back that night.
Step 4: Conclusion
Therefore, the frog escapes the well on the 28th day.
It’s a classic example of why careful attention to conditions on the final day is essential in logic problems.
Final Answer:
The frog will take 28 days to escape the 30-foot well.
Step-by-Step Summary:
| Day | Morning Height (ft) | Climb (ft) | Night Slip (ft) | End of Day Height (ft) | Remark |
|---|---|---|---|---|---|
| 1 | 0 | +3 | -2 | 1 | Starts climbing |
| 2 | 1 | +3 | -2 | 2 | Gaining 1 ft/day |
| 3 | 2 | +3 | -2 | 3 | Continues progress |
| … | … | … | … | … | Pattern continues |
| 27 | 26 | +3 | -2 | 27 | One day before escape |
| 28 | 27 | +3 | — | 30 | Escapes the well |
Why the Frog and Well Puzzle Is Popular?
This puzzle is simple yet deceptive, making it an excellent test of reasoning and comprehension. It is widely used in:
- Aptitude and reasoning tests in competitive exams.
- Math puzzles and logical quizzes.
- Job interviews, especially for analytical roles.
The Frog and Well Puzzle teaches that even small progress, if consistent, leads to success, and it’s a metaphor for persistence and patience.
Similar Logic Puzzles with Answers
If you enjoy thinking puzzles like the Frog and Well Puzzle, you’ll love these other classic logical challenges that test reasoning and calculation.
1. The 100 Prisoners Hat Puzzle – Logic with Parity
Setup: 100 prisoners must guess the color of their own hats.
Answer: By using parity (even/odd count of colors), 99 prisoners are guaranteed to survive.
2. The River Crossing Puzzle – Farmer, Wolf, Goat, and Cabbage
Setup: A farmer must get a wolf, a goat, and a cabbage across a river using a small boat that can carry only one item at a time.
Answer: The correct order is Goat → Wolf → Cabbage → Goat.
3. The Blue Eyes Puzzle – Deduction and Logic
Setup: People on an island do not know their own eye color. A visitor announces that at least one has blue eyes.
Answer: If n people have blue eyes, they all leave on the nth night after deducing it logically.
4. The Monty Hall Problem – Probability at Play
Setup: A player chooses one of three doors, one hiding a car, the others goats. After one goat door is opened, should they switch?
Answer: Yes. Switching increases your chance of winning from 1/3 to ⅔.
5. The Two Guards Riddle – Truth and Lies
Setup: Two guards protect two doors: one safe, one dangerous. One always tells the truth, one always lies.
Answer: Ask either, “If I asked the other which door leads to safety, what would he say?” Then pick the opposite.