Decode the language: Discover the clue hidden in the conversation
Learn how to decode and discover the hidden clue in a conversation through step by step reasoning, applying question, answer and analysis technique.
The riddle
Two friends met in a tramcar after years. Their talks went like this,
— How are you?
— Thank you, I am fine.
— You just got married when we met last about 20 years back. It has been a long time. Any children?
— I have three kids!
— Wow! How old are they?
— Well, if you multiply their ages, you would get 36; but if you add them up, you’d get the number of passengers in this tramcar.
— Got you, but you didn't tell me enough to figure out their ages.
— My oldest kid is a great sports person.
— Aha! Now I know their ages.
Figure out the ages of the three kids.
Time for you to discover the mystery of the ages of the children is 6 minutes.
Hint: Focus on the most important statement. Think exhaustively.
Step by Step Solution to the Tramcar reunion riddle: Learn to Discover Hidden Clue
Step 1. Identifying the most important statement to take up first for analysis:
Follow the fundamental rule in analyzing a collection of statements:
The most important statement in the conversation must be the one with maximum information.
Among all, the key statement stands out:
If you multiply their ages, you would get 36; but if you add them up, you’d get the number of passengers in this tramcar.
Step 2. Role Playing:
- Imagine yourself as the first friend trying to decode this puzzle. Focus on the key statement. This will make your thinking easier.
The first friend must have listed out in his mind, each combination of the three age values with product 36. And then checked the sum with the number of passengers in the tramcar. So you should also follow in his footsteps.
You don't know the number of passengers, but you can at least take the first step.
Step 3. Exhaustive Enumeration of three numbers with product 36: Must not miss any combination
- Start by finding all combinations of factors of 36 and their sums systematically (the friend must have done this, so you must as well). Take up the basis as the prime factors of 36 including 1:
- 36 = 1x2x2x3x3 ⇨ The prime factors (that cannot further be broken up as a product of factors) of 36 are 1, 2, 2, 3 and 3.
- Systematic method to ensure you get all combinations of factors of 36 each with three values representing ages of the three children: Start with 1 as the first factor, then 2 as the first factor, ending with 3 as the first factor.
- 1 + 1 + 36 = 38 (Not possible because of the 20-year gap)
- 1 + 2 + 18 = 21
- 1 + 3 + 12 = 16
- 1 + 4 + 9 = 14
- 1 + 6 + 6 = 13
These are all combinations with 1 as the first factor.
- Move on to 2 and then 3 as the first factor:
- 2 + 2 + 9 = 13
- 2 + 3 + 6 = 11
- 3 + 3 + 4 = 10
These are the feasible combinations with 1, 2 and 3 as the first factor:
Step 4. Identify the reason behind the lingering doubt in the first friend's mind:
The most important question:
Why couldn't the first friend determine the kids' ages even after knowing the product and sum, when the sum was equal to the number of passenger known to him?
Answer: There must have been a deadlock in the seven combinations with two of the combinations having the same sum. That must be the reason the first friend needed further information to clear up his doubt.
Identify these two:
1 + 6 + 6 = 13 and 2 + 2 + 9 = 13.
Step 5. How could the first friend break the deadlock?
The most important question now:
Which answer from the second friend could break the deadlock?
Answer: Identify any specific pattern in the two combinations that stands out. This depends on your ability to spot key patterns, an essential ability in problem solving.
Both the combinations have two ages same and sum also same—this pattern only helped isolate these two combinations as potential candidates for the ultimate solution. You already know it. What else is a new pattern in these two?
Spot the only other pattern in the two combinations that stands out:
- 1, 6, 6 has the two same ages at the end.
- 2, 2, 9 has the two same ages in the beginning.
Hidden clues of this new pattern:
- The combination 1, 6, 6 has two older children of the same age, but the combination 2, 2, 9 has only one oldest child.
- Same way, the combination 1, 6, 6 has one youngest child.
Step 6: Deadlock broken—Hidden Clue Discovered
The only term referring to ages of the children was "oldest" in the second friend's subsequent statement: "My oldest kid is a great sports person." matches the first hidden clue.
He referred to only one oldest kid, not two. Out of the two combinations 1, 6, 6 and 2, 2, 9, the second combination must be the answer.
Answer: The ages of the three children are 2, 2 and 9 years.
Sum up
- First, you have learned the basic rule in identifying the most important statement to focus on.
- Second, you tried to think in the way the first friend thought.
- Third, in doing so, you did what you could—devised a foolproof method and listed out all feasible combinations of ages of the three children having a product of 36.
- Fourth, you could identify the reason behind the lingering doubt in the first friend's mind. You knew at that point, the doubt must have been cleared up by a subsequent statement from the second friend.
- Fifth, in your attempt to find how the first friend could clear up his doubt, you discovered the hidden clue to the puzzle.
- Sixth, you found the answer itself.
This step-by-step technique of forming a doubt, finding the answer, analyzing it, and then forming the next doubt, proceeding in a series of question, answer and analysis is powerful.
To get assured solution with this method, at every stage, you must form the most important question in your mind, gradually narrowing down the possibilities. Our name for this never-failing problem solving technique is the QAA technique of inventive problem solving.
Real-World Application of the Concepts Used
The Tramcar Reunion Riddle showcases several problem-solving concepts that are highly effective in real-world scenarios as well. Here’s how these concepts can be used beyond puzzles, along with supporting resources to explore further:
- Systematic Enumeration
- Listing all possible solutions systematically ensures that no potential option is overlooked. This approach is invaluable in fields like engineering, software development, and project management, where exhaustive analysis is required to identify the best solution.
- Resource: Systematic Approach to Problem-Solving Every Engineer Needs to Know.
- Resource: Decision Trees.
- Identifying patterns, such as the two combinations with the same sum, is a critical skill in data analysis, finance, and scientific research. Recognizing patterns helps in making informed decisions and predicting outcomes.
- Resource: Pattern Recognition in Machine Learning [2025 Guide].
- Resource: Unveiling the Power of Pattern Recognition in Stock Trading.
- The riddle shows how additional information can resolve ambiguity. In real life, gathering more data or asking clarifying questions is essential in decision-making, conflict resolution, and troubleshooting.
- Resource: Embracing Ambiguity: Guidelines and Resources for Success.
- Resource: Embracing ambiguity: Data literacy is more than the ability to read charts.
- The step-by-step reasoning used to solve the riddle mirrors the logical thinking required in fields like law, medicine, and programming. Breaking down complex problems into smaller, manageable steps is a universal problem-solving strategy.
- Resource: How to learn logical reasoning for coding and beyond.
- Resource: Reasoning processes in clinical reasoning: from the perspective of cognitive psychology.
- The riddle highlights the importance of paying attention to subtle clues, such as the mention of the "oldest kid." In real-world contexts, attention to detail is crucial in areas like quality control, auditing, and investigative work.
- Resource: Attention To Detail: Definition, Examples And Tips.
- Resource: Interview Questions for Attention to Detail and Quality Control.
- The riddle encourages thinking outside the box to find hidden clues. This creativity is essential to innovation, marketing, and entrepreneurship, where unconventional solutions often lead to breakthroughs.
- Resource: 12 Powerful Creative Problem-Solving Techniques That Work.
- Resource: Importance of Creativity and Innovation in Business Environment.
By applying these concepts and exploring the linked resources, anyone can enhance their problem-solving skills and approach challenges in both personal and professional settings with greater confidence and effectiveness.
More puzzles to enjoy
From our large collection of interesting puzzles enjoy: Maze puzzles, Riddles, Inventive puzzles, Paradoxes, Mathematical puzzles, Logic puzzles, Number lock puzzles, Missing number puzzles, River crossing puzzles, Ball weighing puzzles and Matchstick puzzles.
You may also look at the full collection of puzzles at one place in the Challenging brain teasers with solutions: Long list.
Enjoy puzzle solving while learning problem solving techniques.