Eureka Moment/Playing With

Basic Trope: A seemingly unrelated stimulus gives a character the inspiration they need to solve a mystery.
 * Straight: Watson X. Position remarks to Amateur Sleuth Shylock Houses that unravelling the case they're working on seems as difficult as selling ice to Eskimos. Houses gets a constipated expression and mutters "Ice? Position, you're a genius!", before convening everyone in the library for The Summation of "The Case Of The Guy Who Was Killed With A Bullet That Was Made Of Ice".
 * Exaggerated: Houses has got literally nowhere until Watson's comment lights a spark that quickly leads Shylock to solve the entire case.
 * Downplayed: The comment leads Shylock to think along slightly different lines. It still takes a lot of careful deduction to solve the case, but he thanks Position for giving him the idea.
 * Justified: Watson is a Puss in Boots, and he lets Shylock think he solves all the cases by making sly hints to him at every opportunity.
 * Inverted: Watson constantly harasses Shylock with irrelevant questions, throwing him off his train of thought just when he thinks he's on the verge of a breakthrough.
 * Subverted: "Ice? Of course!" [Shylock rushes out of the room]. [Shylock returns moments later, clinking his glass of whisky] "Devoting all this thought to the case, would you believe I was completely unable to think of a way to cool down my Scotch!"
 * Double Subverted: "...Wait a moment - Scotch... Scotland... North... Arctic... Ice... Snow... Cold... Freezing... Ice... Eureka!"
 * Parodied:
 * Placebo Eureka Moment - Watson doesn't say a word as Shylock explains his thoughts on the case, but when the detective manages to inspire himself in the process, he praises his bemused sidekick for breaking the case for him.
 * Shylock takes an incredibly long time to process his Bat Deduction, during which we see Position rolling his eyes and checking his watch.
 * Deconstructed: After one inane non sequitur too many, Shylock lets Watson go, saying he doesn't pull his weight and just distracts his friend from the case at hand.
 * Reconstructed: ...However, without him, Shylock can't solve a single case. He comes to realise that bouncing ideas off his partner was central to his thought process, and hires him back with the closest he can get to a heartfelt apology.
 * Zig Zagged: Most of Watson's comments are pure comic relief, Parrot Exposition, Let Me Get This Straight..., and other Audience Surrogate techniques. But once in a while, the Dumbass Has a Point and says something that helps solve the case, while occasionally he even works something out that his Insufferable Genius friend hadn't even considered.
 * Averted: All Shylock's cases are solved with cold, linear deduction from start to finish.
 * Enforced: "People keep asking what Shylock keeps Watson around for if he never says anything useful, but we don't want to make him look like he's thought of anything that Shylock hasn't... what if he says something in ignorance that inspires Shylock to have a flash of genius?"
 * Lampshaded: "Shylock, you're doing that face again."
 * Invoked: Shylock only keeps Watson around to bounce ideas off. He's a Straw Vulcan and knows it, and he finds it useful to keep someone with a more disorganised mind around to speak the "wisdom of fools".
 * Exploited: ???
 * Defied: "What are you looking at me like that for? Do you think there's something profoundly significant in your babbling about "ice to Eskimos"? Shut up and let me think!"
 * Discussed: "Come on, Position, this is where you're supposed to say something naively insightful that will lead me to solve the case!"
 * Conversed: "I don't know why Dr House is so set against clinic duty when it's how he solves literally all of his cases..."
 * Played For Laughs: "I don't know, maybe the bullet was made of ice?" "Ice? Ice... Of course! I have it now! The bullet was made out of ice!"

Back to Eureka Moment.