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The Train Ride (The Train Journey in the UK version) is a puzzle in Professor Layton and the Diabolical Box.

Puzzle

US Version

An unknown number of people are riding a train. At the first station the train pulls into, 1/6 of the people on board get off. At the next station, 1/5 of the remaining passengers get off. This pattern continues so that at the next stations 1/4 get off, then 1/3, and then 1/2. Then, at the final station, all passengers remaining on the train exit as well.

Assuming no one got on the train during the ride, what is the fewest number of people that could have been riding on the train when it set out?

UK Version

A number of people are on a train. At the first station the train pulls into, 1/6 of the people on board get off. At the next station, 1/5 of the remaining passengers get off. This pattern continues so that at the next station 1/4 get off, then 1/3 and then 1/2. Then, at the final station, all remaining passengers get off the train.

Assuming no one got on the train during the journey, what is the lowest number of people who could have been on the train when it set out?

Hints




Click a Tab to reveal the Hint.

US Version

Since the puzzle tells you that no one got on the train during the ride, it's safe to say that the number of passengers on the train never increased.

UK Version

Since the puzzle tells you that no one got on the train during the journey, it's safe to say that the number of passengers on the train never increased.

Since 1/6 of the passengers get off at the first station, you know the number must be divisible by six. Start by choosing a number that's divisible by six and see what happens.

US Version

The principle by which this puzzle is solved should become evident soon.

UK Version

The principle by which this puzzle is solved should soon become evident.

US Version

Imagine that 30 passengers are on the train when it embarks. At the first station, the train loses 1/6 of its passengers, meaning five people get off. At the next station, 1/5 of those remaining, or five people, get off. At the next station, 1/4 of those remaining, or five more people, get off.

Do you notice a pattern here?

UK Version

Imagine that 30 passengers are on the train when it departs. At the first station, the train loses 1/6 of its passengers, meaning five people get off. At the next station, 1/5 of the remaining 25, or five people, get off. At the next station, 1/4 of the remaining 20, which is to say five more people, get off.

Do you notice a pattern here?


Solution

Incorrect

Too bad!

US Version

Think hard about the clues you've been given and try again. This puzzle comes together quite easily once you realize a certain simple principle.

UK Version

Think hard about the information you've been given and try again. This puzzle comes together quite easily once you realise a certain simple principle.

Correct

Good work!

US Version

If you assume the train started out with six passengers, then only one person would have to get off at each station. This puzzle can be really tough if you don't remember to reduce the number of people remaining on the train at each station along the way.

UK Version

If you assume the train started out with six passengers, then only one person would have to get off at each station.

This puzzle can be really tough if you don't remember to reduce the number of people remaining on the train at each station along the way.

DB019S

A big thanks to http://professorlayton2walkthrough.blogspot.com

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