The Late Train and the Man Ten Minutes Early

Difficulty ★★☆about 5 minLogic PuzzleAlibiTimetables

A murder at the next station. The suspect could not have made it on the delayed train, yet he is the culprit. How did he travel?

Case Record

At exactly noon, an office worker named Miyashita was stabbed to death on the pavement in front of Minamihama Station.

The suspect is his colleague Otsuki, who lives right next to the neighboring Kitahara Station. The trip from Kitahara to Minamihama takes 6 minutes by train. Normally the train leaves at 11:50 and arrives at 11:56.

Otsuki is a stickler for time and is always on the platform ten minutes before a train departs. That day he was seen on the Kitahara platform at 11:40.

But heavy rain delayed every train by 20 minutes. Buses were suspended and the bike-rental service at the station was suspended. Otsuki insists, "There is no way I could have caught a train." He had no accomplice. Also, Otsuki had injured his leg a few days earlier and could not run.

Your question

How did Otsuki reach the front of Minamihama Station by noon?

Case Files

Evidence

E-1Kitahara gate cameraAt 11:43 Otsuki is seen leaving the gate. He did not board a train.
E-2Service noticeAll trains 20 minutes late due to heavy rain. Next train leaves 12:10.
E-3Scene at MinamihamaMiyashita was stabbed on the pavement. A passer-by heard a scream at exactly 12:00.

Diagram

Timeline

11:40Otsuki is seen on the Kitahara platform.
11:43He is filmed leaving through the ticket gate.
12:00Miyashita is stabbed on the pavement outside Minamihama Station.
12:16The delayed train reaches Minamihama.

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

What time does the delayed train reach Minamihama? Compare it with the time of the murder.

Open hint 2

Remember the gate camera. Otsuki left the gate without boarding a train.

Open hint 3

How long does 5.2 km take on foot and by car?

Solve It

Your question

How did Otsuki reach the front of Minamihama Station by noon?

Choose the answer closest to the truth.

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The Truth

He left through the ticket gate and went to Minamihama Station by car, such as a taxi

The answer is: he left through the ticket gate and went to Minamihama Station by car, such as a taxi.

The delayed train left Kitahara at 12:10 and reached Minamihama at 12:16, too late for a noon murder. But the Kitahara ticket-gate camera shows Otsuki leaving through the gate at 11:43. Learning the rain would delay the trains, he gave up on the train.

The distance is 5.2 km. Otsuki could not run because of his injured leg, so on foot it would take about 60 minutes, but about 14 minutes by taxi, including waiting, so he could be at Minamihama Station by 11:57. The assumption that "someone who would make it on a normal train cannot make it on a delayed one" hid the other option: a car.

Diagram of the solution

Key Points

"The train was late" does not rule out means other than the train
List the travel time for each means and compare it with the time of the crime
When unusable means (bus, rental bike) are stated outright, what remains is the answer

Why people get fooled

Traits like "a stickler for time" and "on the platform ten minutes before departure" make you picture a train rider. Staring at the train timetable erases other means of travel from your mind.

Similar tricks

The "choose a different transport to break a timetable alibi" type
The "habit becomes an assumption" type

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