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.**

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 2^{nd} 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.

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