logics

Answers

1.Emily had used the mute button during her conversation with Anna so that all Anna heard was: "call...help...emergency...please hurry". Anna, sensing something was wrong, called the police and told them Emily's address. The police were able to come to Emily's house in time to catch the perpetrator.

2.Detective Drosnin tried arranging the letters in Ms. Gray's email the way she described arranging the kids at her school, into rows of twenty one. Then he took a look at the second column like she suggested:

t H i s m o r n i n g i t r i e d a f u n
n E w s e a t i n g s t y l e f o r t h e
k I d s d u r i n g t h e m o r n i n g a
s S e m b l y i h e l p e d a r r a n g e
t H e m i n t o r o w s o f t w e n t y o
n E t h e k i d s d i d n t c a r e b u t
i R e a l l y l o v e d i t i l i k e d t 
h E s e c o n d c o l u m n t h e b e s t

No wonder she didn't invite him in!

3.Pete told them to form a circle around him. All the squad was facing in at Pete, ready to shoot, when they realized that everyone who missed would likely end up shooting another squad member. So no one dared to fire, knowing the risk. Thus at sundown he was released.

4."Who has been your source for information on this case?" Chief Graham asked news reporter Sheila Rivers. 

"What, do you not remember talking to me? I've gotten all my info from you. Which hasn't been much, I have to say," replied Ms. Rivers impatiently.
"Right. Have you gotten any more details from anyone else?"
"No, only what you've given me. Why, do you have more for me?"
"Yes. We have a lead suspect. Do you remember what you reported earlier this evening? That the town's richest man was murdered late last night?"
"Of course."
"How late?"
"Well...Oh. Rats."
"Rats indeed. The last time anyone had any contact with the victim that we know of was last Saturday, and the time of death is impossible to determine due to Mr. Hampton's body being preserved in the freezer and his tendency to let his mail pile up. So the best estimate we have for the time of the murder is some time between Saturday and this morning when the body was found. But somehow you've determined a much more specific time of death. When I heard you say that...well, a little while after I heard you say that, I realized that either you or your source knows way more than an innocent person should. And now you've told me that it's you! You might as well confess, because let's face it, this story has gone on long enough already." 
"Alright, fine. Do you know how hard it is to be a reporter in this stupid, boring town!? I'm so SICK of having nothing more important to report on than the high school's class president elections, or this year's dog petting contest. It was DRIVING ME CRAZY! I was DYING for a real story! Then I realized...why should I be the one to die?"

5.Mark Crimson 

"?" = question MARK, so the note on the door reads "Question Mark Crimson. He broke your window."