SORRY FOR THE GAME PLAYING. I just wanted to make a point to show you folks the answers are infinite and no sane human being can come up with the answer:
1. The case where the two men had their heads cut off.
The two older Queens invited a younger man for dinner. The young guy thought the older guys 'turned' his father. He has dinner. Kills both men. He knew they were big baseball fans. The World Series was on. He put the both heads in one lap because he knew they were big fans and he didn't want them to miss the game.
The pinkie under the arm. He said he knew this would drive the cops crazy trying to figure out why. It didn't bother me at all. Chopping off 2 heads and putting them in the lap of one of them was nutty enough for me. But the guy was right because the other guys were going nuts.
2. The guy in the auto shop. Two guys went in to rob the place. Just a simple robbery. They were so high they forgot why they went there. One nut job can't figure out why and puts his gun on the upper right arm of the victim and screams: "Now you die." Fires the gun....bullet goes thru the arm and into the body. The crack heads escape. Only pure luck with a little of good police work closes the case.
3. Saved the best one for last: The nut job killer was paying hookers $5.00 for used condoms. The deal was to ask their customer for the condom or pick it up when it was discarded. He bought 8 of them. Kills the gal and sprinkles the semen of the 8 used condoms on the body. Never did get the rest of the story as to WHY this nut job did it. It didn't matter why he did it, it only mattered he did it.
I tell you the above to try to demonstrate there are NO answers in most cases that a reasonable and sane person can come to in a case like LISK.
So, you say, as long as nobody asks the right questions the riddles are unsolvable and therefore nobody should ask the right questions? Somehow this whole riddle idea is a bit off the case here, but well, nothing about a little play time.
Number one turned out to be some kind of hate crime, which was obvious after someone looked in the victim's background. But of course, that part wasn't included in your riddle. So ... after asking the right questions, the riddle was obviously solvable. I mean, police got the guy, didn't they? So all this story proves is the importance of victimology.
Number two: No robbery made everyone think of course of a personal motive. But you didn't tell about other crime scene details. Obviously police got those two also, after asking the right questions, so this one was only unsolvable because you left essential information out. Which underlines, how important details can be.
Number three: It matters. After all, the crime scene showed sperm from 8 donors. So at this point, either it was a gangrape or forensic counter measure. But then you added, only one raped her, which is a hindsight information. So, obviously, police caught that guy. Means, there had to be at least one other details, that made someone ask the right questions.
So all three cases were solved because someone asked the right questions. To dismiss all theorizing and therefore all asking, didn't solve any of those cases, right?