Yea! You are right!
The actual explanation goes like this:
The woman was actually killed at the first floor. This is because, when she is paranoid about someone going to kill her, she will be relieved when she found out that the killer has not yet made it to the third story to kill her. She will immediately press the button to the lobby and rush out to the nearest police station.
The man did not kill the woman at the first level when he went in with the woman because of the security camera. If the man were to kill her on the third floor, it would be the same to kill her on the first floor - He would be stabbing her inwards from the outside of the lift. The only reason he did not kill her at the first floor was because he could not. The best reason is that there is a security camera and he did not want to be caught on tape. Therefore, he would not kill the woman on the third level as well.
Him holding the knife running up the third level is just a scare. It made the woman believe he was going to kill her at the third level, which makes her panick and get to the first level. All the man needed to do, was to pretend to climb halfway to the third level and immediately run to first level once she is out of view. A man runs faster than the lift for first few three or four levels. The woman was killed when she ran out of the lift and out of the apartment where there are no more security cameras.
How to save her life:
This man is not a stupid man. He is smart. So he will not expect to be tricked by his own trick.
What the woman should do is, when she reaches the third level, and found out that guy is not there yet, she should wait for the door to close naturally. Wait for a while then press the top floor of the building.
This gives a misconception that the woman has exited the lift. The man would panick and run up to the third story to check. And when he realises that the woman has not exited, he will be sure the woman has gone up to the highest level of the building. This time, he will either choose to press the lift and follow her up, or run up to the highest floor, lets say 13th level.
Either way, the woman is already at the highest floor. She will then throw out some distinguishable belongings there. Then she goes back to the lift and goes down two to three levels and throw something out again. When the man reaches the top level, he will be made to consider two choices - the woman has exited or it is a bluff. The woman now has a half half chance of escaping.
In the case the man thinks its a bluff and runs down the stairs to check, he will again stumble on the same choice when he sees the woman's belongings. Now, the man must choose again. This time, the woman's probability of escaping is another half half.
Continue for all the levels, lets say every two levels, 13, 11, 9, 7, 5, 3. Then the woman goes out of the first level and runs to the police station.
Lets calculate the probability of the woman to be caught.
1/2 (13) x 1/2 (11) x 1/2 (9) x 1/2 (7) x 1/2 (5) x 1/2 (3) = 1/64 which is really really small.
Yep. Thats the end of the analysis.
Thank you very much for reading. Haha