The following has absolutely nothing to do with the topic at hand, but I couldn't resist.

The portion of your post quoted above immediately reminded me of an episode the old TV show, "Get Smart", with Don Adams. I'm sure you remember it.

Anyway, there was a classic episode in which Maxwell Smart hooks up with the famed Hawaiian detective Harry Hoo, who was an hilarious send-up of Charlie Chan.

Sure enough, I was able to find a transcript of the scene on a Charlie Chan website. It's pretty funny, I think. The part that I put in bold is what your post reminded me of.

Isn't it amazing what sticks in your mind after forty years?

MAX: Uh, what puzzles me in this case, Inspector Hoo, is the motive for the murder.
HOO: Oh, correction. This is not case of murder, Mr. Smart. Is case of rovvery.
MAX: Rovvery?...That’s amazing. But how can you say it’s robbery, Mr. Hoo? I mean, the man was found dead with a hundred dollars in his wallet.
HOO: Humble to beg pardon, Mr. Smart. Suppose victim’s pocket originally contained one hundred and one dollar.
MAX: By George, you’re right! They took the dollar and left the hundred dollars to throw us off the track!
HOO: You are apt pupil, Mr. Smart.
MAX: Yes, of course. And then they murdered him so we wouldn’t find out about the rovvery. (HOO looks at him funny.)
HOO: It is widely written, Mr. Smart: dead men tell no tales. (MAX is visibly impressed. HOO lifts the blanket covering the body.) Mr. Smart, you are man of some perception. What do you notice about man on floor?
MAX: He’s not breathing.
HOO: Which presents two possibilities. One: man has gone to visit honorable ancestors.
MAX: Or?
HOO: Man very good at holding breath. Do you notice anything else unusual, Mr. Smart?
MAX: No, I don’t think so.
HOO: Your eyes see, Mr. Smart, but they do not observe.
MAX: I don’t think I follow you, Mr. Hoo.
HOO: Observe closely, Mr. Smart. Murdered man dressed in business suit. Gray jacket and pants. Black socks and shoes. Striped necktie. Silver tie clasp.
MAX: Looks pretty good.
HOO: Then why, I ask you, Mr. Smart, why is he not wearing shirt?
MAX: By golly, you don’t miss a trick, do you? You know, a lot of people wouldn’t have noticed that little detail.
HOO: That is why it is wisely written, Mr. Smart: bird in hand gathers no moss. (spots something on the floor; steps over the body to pick it up) Ah, so.
MAX: Is it a clue, Hoo?
HOO: It is evidence left by murderer, Mr. Smart.
MAX: It’s a button.
HOO: Which presents two possibilities: one, victim tore button from murderer’s coat during struggle.
MAX: Or?
HOO: Is button from...my jacket. Sleeve. (examines his cuff; wanders away. MAX follows him)
MAX: Tell me, Mr. Hoo, do all Hawaiian detectives wear white suits?
HOO: No. I began to wear white suit in Hawaii when I was employee of ice cream firm.
MAX: Well, it’s very attractive.
HOO: You should see my cleaning bills. Tell me, Mr. Smart, how you think murder was committed.
MAX: Two possibilities. (HOO looks at him funny again.) One: he was killed by a .22 caliber pistol at long range by a short man who was a stranger to him.
HOO: Or?
MAX: He was killed at close range by a knife used by a woman he knew who was over six feet tall.
HOO: Amazing...Ah so. (crosses to table, picks up an ashtray)
MAX: Found something, Mr. Hoo?
HOO: Perhaps, Mr. Smart. Notice the ashtray containing two cigarettes. (holds up three fingers . MAX and HOO look at them. HOO puts one down.)
MAX: I see. Well, then that means there was someone here in the room when the victim was killed. Perhaps even the murderer.
HOO: Moment please.
MAX: Moment please?

HOO: Once again worthy CONTROL agent leap at too obvious a conclusion. If victim were non-smoker, there could have been two smokers in the room with him.
MAX: Well, that’s true.
HOO: Perhaps two smokers and one non-smoker.
MAX: Moment please.
HOO: Moment please?
MAX: Perhaps there were two smokers and two non-smokers.
HOO: Perhaps there were two smokers and FOUR non-smokers.

MAX: Well, then, what you’re saying, Mr. Hoo, is that there could have been as many as fifty people in the room with the victim when he was killed, provided only two of them were smokers.
HOO: Exactly. (puts down ashtray, crosses to other side of the room)
MAX: Boy, it must have been crowded in here. (two policemen walk by and pick up their still-smoking cigarettes)