How to provide a simple example to the requirement of falsifiability in the scientific method to a novice audience?

(I once posted this ques­tion on academia.stack­ex­change, but it was deemed to be off topic there. I hope it would be more on-topic here)

I would like to in­tro­duce the ba­sics of the sci­en­tific method to an au­di­ence un­fa­mil­iar with the real mean­ing of it, with­out mak­ing it hard to un­der­stand.

As the sus­pected knowl­edge level of the in­tended au­di­ence is of the type which com­monly thinks that to “prove some­thing sci­en­tifi­cally” is the same as “use mod­ern tech­nolog­i­cal gad­gets to mea­sure some­thing, af­ter­wards in­ter­pret the re­sults as we wish”, my ma­jor topic would be the se­lec­tion of an ex­per­i­men­tal method and the im­por­tance of falsifi­a­bil­ity. Wikipe­dia lists the “all swans are white” as an ex­am­ple for a falsifi­able state­ment, but it is not prac­ti­cal enough. To prove that all swans are white would re­quire to ob­serve all the swans in the world. I’m search­ing of a sim­ple ex­am­ple which uses the sci­en­tific method to de­ter­mine the work­ings of an un­known sys­tem, start­ing by form­ing a good hy­poth­e­sis.

A good ex­am­ple I found is the 2-4-6 game, cul­mi­nat­ing in the very catchy phrase “if you are equally good at ex­plain­ing any out­come, you have zero knowl­edge”. This would be one of the best ex­am­ples to illus­trate the most im­por­tant part of the sci­en­tific method which a lot of peo­ple imag­ine in­cor­rectly, it has just one flaw: for best effect it has to be in­ter­ac­tive. And if I make it in­ter­ac­tive, it has some non-neg­ligible chance to fail, es­pe­cially if done with a broader au­di­ence.

Is there any sim­ple, non-in­ter­ac­tive ex­am­ple to illus­trate the prob­lem un­der­ly­ing the 2-4-6 game? (for ex­am­ple, if we had taken this naive method to for­mu­late our hy­poth­e­sis, we would have failed)

I know, the above ex­am­ple is mostly used in the topic of fal­la­cies, like the con­fir­ma­tion bias, but nev­er­the­less it seems to me as a good method in grasp­ing the most im­por­tant as­pects of the sci­en­tific method.

I’ve seen sev­eral good posts about the im­por­tance of falsifi­a­bil­ity, some of them in this very com­mu­nity, but I did not yet see any ex­am­ple which is sim­ple enough so that peo­ple un­fa­mil­iar with how sci­en­tists work, can also un­der­stand it. A good work­ing ex­am­ple would be one, where we want to study a fa­mil­iar con­cept, but by for­get­ting to take falsifi­a­bil­ity into ac­count, we ar­rive to an ob­vi­ously wrong (and prefer­ably hu­morous) con­clu­sion.

(How I imag­ine such an ex­am­ple to work? My fa­vorite ex­am­ple in a differ­ent topic is the egg-lay­ing dog. A dog en­ters the room where we placed ten sausages and ten eggs, and when it leaves the room, we ob­serve that the per­centage of eggs rel­a­tive to the sausages in­creased, so we con­clude that the dog must have pro­duced eggs. It’s easy to spot the mis­take in this ex­am­ple, be­cause the image of a dog lay­ing eggs is ab­surd. How­ever, let’s re­place the ex­am­ple of the dog with an effec­tive medicine against heart dis­eases where some­one no­ticed that the chance of dy­ing of can­cer in the next ten years in­creased for those pa­tients who were treated with it, so they de­clared the medicine to be car­cino­genic even though it wasn’t (peo­ple are not im­mor­tal, so if they didn’t die in one dis­ease, they died later in an­other one). In this case, many peo­ple will ac­cept that it’s car­cino­genic with­out any sec­ond thought. This is why the ex­am­ple of the egg-lay­ing dog can be so use­ful in illus­trat­ing the prob­lem. Now, the egg-lay­ing dog is not a good ex­am­ple to raise aware­ness for the im­por­tance of falsifi­a­bil­ity, I pre­sented it as a good and use­ful style for an effec­tive ex­am­ple any lay­men can un­der­stand)