Crucial Support of a Girlfriend - Puzzle

A man escapes from jail with help from his girlfriend. Four girls are accused of being the man's girlfriend. His girlfriend is lying. Two girls are innocent and telling the truth. The other girl is the man's sister who is helping the girlfriend lie. 

Who is the man's sister?

Amanda: "Melinda is his girlfriend."

Vanessa: "Eva is lying."

Eva: "Amanda is lying."

Melinda: "Vanessa is not his sister."

Know who is man's sister! 

Crucial Support of Girlfriend Puzzle : Solution

What was the puzzle?

What we know so far.

A man escapes from jail with help from his girlfriend. Four girls are accused of being the man's girlfriend. His girlfriend is lying. Two girls are innocent and telling the truth. The other girl is the man's sister who is helping the girlfriend lie. 

And statements of four girls are - 

Amanda: "Melinda is his girlfriend."

Vanessa: "Eva is lying."

Eva: "Amanda is lying."

Melinda: "Vanessa is not his sister."

Now, for a moment, let's assume Amanda is telling the truth. Then Melinda must be man's girlfriend who is lying. Therefore, Vanessa must be man's sister who is lying in support of man's girlfriend Melinda. 

So, Vanessa's lying statement suggests that Eva must be telling the truth. But as per Eva, Amanda is lying which is contrary to our initial assumption that Amanda is telling the truth.

So, Amanda must be lying.

If Amanda is lying then Eva must be telling the truth. And if Eva is telling the truth then Vanessa must be lying. 

With that we have 2 lying girls viz. Amanda and Vanessa & Eva as innocent girl telling the truth. Therefore, other innocent girl must be Melinda who must be telling the truth. 

So, as per innocent Melinda, Vanessa isn't a man's sister, hence Amanda must be. And Vanessa is man's girlfriend.

Story of Man Having 2 Girlfriends

A man who lives in Middletown has two girlfriends, one in Northtown and one in Southtown. 

Trains from the Middletown train station leave for Northtown once every hour. Separate trains from the station also leave for Southtown once every hour. No trains go to both Northtown and Southtown.

Each day he gets to the Middletown train station at a completely random time and gets onto the first train that is going to either Northtown or Southtown, whichever comes first.

After a few months, he realizes that he spends 80% of his days with his girlfriend from Northtown, and only 20% of his days with his girlfriend from Southtown.

How could this be?

THIS could be the reason behind it! 

Behind Unfair The Number of Visits

What's the story behind the title?

The man arrives at Middletown train station at a completely random time of the day. 

Let's take a look at what happens when he arrives at random time of the day.

After arrival on the station, he is likely to get the train in next hour for sure.

After arriving at random time, there are 80% chances that the first train arriving at the station is heading towards Northtown and 20% chances are there the train is heading towards the Southtown. 

That is there has to be 80% minutes of hour (80% of 60 = 48 minutes) where the first train after is heading towards Northtown and 20% minutes of hour where the next train is heading towards Southtown (20% of 60 = 12 minutes).

So, the trains heading towards the Southtown must be scheduled 12 minutes apart from train heading towards the Northtown.

For example, if trains heading to Northtown are scheduled at 9:00 AM, 10:00 AM, 11:00 AM.......etc then the trains to the Southtown must be scheduled at 9:12 AM, 10:12 AM, 11:12 AM.....etc.

With arrival in 48 minutes past 9:12 AM, 10:12 AM etc, he must be getting the Northtown train and if arrived in 12 minutes past 9:00 AM,10:00 AM etc, he would be getting the Southwest train.

Remember, the timing given are for examples only. The Northwest trains may be scheduled at 9:48 AM, 10:48 AM,......etc and Southwest may be scheduled at 10:00 AM, 11:00 AM.

Key is they leave 12 minutes apart, so that 60 minutes of hour are divided into 48 minutes ahead of Northwest train and 12 minutes ahead of Southwest train.