*Can you understand the chirping between two sparrows?*

## Key to the riddle is hidden in the two friends' conversation (in coded language)

Discover the critical information hidden in the two friends' conversation by analysis and reasoning. Ask key questions, discover answers and analyze.

### 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.

Have you also figured out the ages of the three kids?

**Time for you** to discover the mystery of the ages of the children is **6 minutes **(but if you need, do take more time, solve it anyway).

If you can solve in time, both you and I will be happy,** because you will learn the art of deductive reasoning**, *unerringly homing in to the critical clue and then on to the solution yourself.*

### Step-by-Step Solution to the Tramcar reunion riddle

#### 1. Discovery of key Information hidden in the conversation**:**

The most important statement in the conversation must be the one with maximum information. Among all, the 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."

#### 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.

#### 3. Exhaustive Enumeration: Follow a method so that you miss no combination at all

- Start by
**finding all combinations of factors of 36 and their sums***systematically***(the friend must have done this, so you must as well):**36 = 2x2x3x3: - 1 + 1 + 36 = 38 (Not possible due to the 20-year gap)
- 1 + 2 + 18 = 21
- 1 + 3 + 12 = 16
- 1 + 4 + 9 = 14
- 1 + 6 + 6 = 13 (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 (All combinations with 2 and 3 as the first factor)

#### 4. Form your Key question and doubt:

- Why couldn't the first friend determine the kids' ages even after knowing the product and sum?

#### 5. Answer to the key question: Recognize the Deadlock:

- Realize that
**a pair of factor combinations must have the SAME SUM**, causing the deadlock:

1 + 6 + 6 = 13 and 2 + 2 + 9 = 13 (one of these two will be the answer)

#### 6. Form your Second Key Question and doubt:

- Which answer from the second friend did break the deadlock?

#### 7. Answer to the second doubt: Utilize Contextual Information:

- The statement having the final clue must have referred to the comparative ages of the children (
**because both combinations have two children of same age**):

- Discover that the term "oldest" in the second friend's statement:

— "My oldest kid is a great sports person" — is crucial.

#### 8. Unravel the mystery of the Puzzle: Use simple reasoning and Form your answer:

- The second friend has ONE "oldest" son.
- This information eliminates one combination (1 + 6 + 6) where there are two elder sons.
- Therefore, the ages of the kids are 2 years, 2 years, and 9 years.

Wasn't it fun to solve!

Hold on for a moment. Don't go away, yet.

### Let us see what we have learned in solving the puzzle by analysis and reasoning

We've learned a lot from this **logic puzzle**. It's about finding a solution **based on given statements**.

- First, we realized the most important statement contains the maximum information. Then, we understood the importance of putting ourselves in someone else's shoes to solve it.
- The first friend in the puzzle would start by listing all possible age combinations for the children. We followed this step too, which is called
**exhaustive enumeration**. It's crucial to be systematic**(following a method)**when doing this. I call it the**Principle of Exhaustiveness.**If you get used to thinking this way, other problems become easier. - Next, we thought about
**why the first friend couldn't find the solution**even when he knew both the product and sum of the ages. We figured out that**two combinations had the same sum of ages**, causing a deadlock. - We then asked which statement from the second friend helped to break the deadlock. It must be the one mentioning the ages of the children as both the two candidate combinations have two children with same age.
- By
**focusing on the word "oldest,"**we realized there**must be one oldest child.**This is**basic reasoning using context based English.** - Once we understood this, the solution became clear.

The technique of forming doubts, finding answers, analyzing them, and then asking more questions is powerful. I call it **QAA technique of inventive problem solving**. I've used it successfully in many problem-solving situations, **including real-life ones**.

### More puzzles to enjoy

From our large collection of interesting puzzles enjoy: * Maze puzzles*,

**Riddles**,

*,*

**Mathematical puzzles***,*

**Logic puzzles***,*

**Number lock puzzles***,*

**Missing number puzzles***,*

**River crossing puzzles***and*

**Ball weighing puzzles***.*

**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.*