# Popular Train Math Puzzle ?

Math riddles help you improve your numerical and analytical skills. Even though a puzzle appears absurd or odd, it can still be challenging; framing a mathematical subject as a riddle forces students to use critical and analytical thinking in novel ways, which improves their overall comprehension. Here is an interesting math riddle, Even though this puzzle looks very simple in the first view it can have multiple interpretations.

There are some people on a train. 19 get off at the first stop. 17 get on. Now there are 63 people on the train. How many were on the train, to begin with?

Give it a try before checking the solution.

Solution

Even though this puzzle looks very simple in the first view it can have multiple interpretations.

I am going to provide you three interpretations of how someone can think about this puzzle, this will help in understanding the approach required to solve these kinds of puzzles.

INTERPRETATION 1

A simple way to look into the problem is through the math way. As per the puzzle, the People remaining on the train after the addition and subtraction of passengers is 63

And People who got in from the first stop = 17

and the People who got off from the first stop = 19

Just do simple math, that is ... remaining passengers - newly added passengers => this will fetch you the old passengers on the train. That is => 63 - 17 = 46

Now... add... old passengers + passengers who got off from the first stop => That is, 46 + 19 = 65

So there must have been 65 people on the train in the beginning. This answer is accepted by many people, but since this is a brain teaser we must be clear on the assumptions.

INTERPRETATION 2

Let’s check the 2nd way of looking into the problem.

Ã¼ There are 63 people now on the train after the first station. It represents a combination of new and old passengers.

Ã¼ The 17 people that get on the first station are new passengers and are not considered to be "on the train to begin with".

Ã¼ The 19 people that get off were old passengers but are no longer on the train.

If none got off, the number of people that were on the train originally, to begin with, is 46 + 19 or a total of 65.

Now there are 63 people on the train. How many were on the train, to begin with? This can be interpreted as, how many old passengers remain on the train. (those were on the train, to begin with)

Thus Solution is: People that are on the train now are, 63 - 17 = 46 (and these are the remnants of those who were on the train, to begin with)

Thus, the Final Answer is 46 as per this interpretation.

INTERPRETATION 3

let's get into the final interpretation, many people think that, it is impossible to tell the answer to this puzzle with this information. why they think like this is because, the question doesn’t state when the 17 people got on the train, how many stops it has passed, or whether any more people departed or boarded in the meantime.

Assuming the 17 people got on to the train at the first stop, when 19 people also departed, and the train has not yet left the station, it would be 65 people on the train when it pulled into the first stop.

However, to begin with, there would be no people on the train. The train would be empty before beginning any journey.

This puzzle can have other interpretations, do share your answer in the comment section. what is important in these kinds of puzzles is to think out of the box, this puzzle can have more than one correct answer thus the expectation is the correct approach opted to solve this puzzle.