Anwara, Bharati, Colin and Tarun commute by different modes of transport namely, Cycle (C), Autorickshaw (A), Bus (B) and Train (T). The initials of the mode of transport and the name of the person match in exactly two cases. If Tarun travels by Train, and Colin rides neither an Autorickshaw nor a Bus, then
Anwara rides a Bus.
Commute Puzzle Analysis
This logic puzzle involves four people – Anwara, Bharati, Colin, and Tarun – who use four different modes of transport – Cycle, Autorickshaw, Bus, and Train. The key condition is that the initial of the person's name matches the initial of their mode of transport in exactly two cases.
Given Information
- People: Anwara (A), Bharati (B), Colin (C), Tarun (T)
- Modes: Cycle (C), Autorickshaw (A), Bus (B), Train (T)
- Constraint 1: Exactly two people have initials matching their mode's initial (e.g., Anwara rides Autorickshaw - A rides A; Colin rides Cycle - C rides C).
- Constraint 2: Tarun travels by Train (T). This is one of the matching cases (T rides T).
- Constraint 3: Colin rides neither an Autorickshaw (A) nor a Bus (B).
Deducing the Solution
We know Tarun travels by Train (T rides T). This is one of the two matching cases based on initial. So, we need exactly one more match among Anwara, Bharati, and Colin.
Colin does not ride Autorickshaw (A) and does not ride Bus (B). The available modes for Colin are Cycle (C) or Train (T). However, Train is already assigned to Tarun. So, Colin must ride Cycle (C).
- Colin rides Cycle (C). Let's check the initial match: C rides C. This is a match!
Since Tarun riding Train (T rides T) was the first match, and Colin riding Cycle (C rides C) is the second match, we have found exactly two matches. This means that Anwara and Bharati must travel by modes whose initials do NOT match their own initials.
Current assignments:
- Tarun: Train (T rides T - Match)
- Colin: Cycle (C rides C - Match)
Remaining people: Anwara (A), Bharati (B)
Remaining modes: Autorickshaw (A), Bus (B)
Anwara (A) must ride either Autorickshaw (A) or Bus (B). Bharati (B) must ride the other remaining mode.
- If Anwara rides Autorickshaw (A), this would be A rides A, which is a match. But we already have two matches (T-T and C-C), and we cannot have a third. So, Anwara cannot ride Autorickshaw.
- Therefore, Anwara must ride Bus (B). This is A rides B, which is not a match (A <> B). This fits the requirement that Anwara's initial should not match her mode's initial.
If Anwara rides Bus (B), then Bharati must ride the remaining mode, which is Autorickshaw (A). This is B rides A, which is not a match (B <> A). This also fits the requirement that Bharati's initial should not match her mode's initial.
Summary of Assignments
| Person | Mode of Transport | Initial Match? |
|---|---|---|
| Anwara (A) | Bus (B) | No (A <> B) |
| Bharati (B) | Autorickshaw (A) | No (B <> A) |
| Colin (C) | Cycle (C) | Yes (C = C) |
| Tarun (T) | Train (T) | Yes (T = T) |
Checking the constraints:
- Exactly two matches: Colin-Cycle (C-C) and Tarun-Train (T-T). Yes, exactly two matches.
- Tarun travels by Train: Yes.
- Colin rides neither Autorickshaw nor Bus: Colin rides Cycle. Yes, this condition is met.
All conditions are satisfied by this set of assignments.
Based on this deduction, Anwara rides a Bus.
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