This is the (possibly true) explanation of the trick that P&T gave in Cruel Tricks for Dear Friends:
Jura Craa jnf va gur guebrf bs jevgvat gur "Vaivfvoyr Guernq" fubeg fgbel, ur pnzr gb zr bar qnl naq nfxrq zr vs V xarj bs n gevpx gung jbhyq fvzhyngr gur cerfrapr bs vaivfvoyr guernq va gur cvgpu. Ab fhpu gevpx rkvfgrq. "Qbrf vg unir gb jbex?" V fnvq.
"Bs pbhefr abg. Vg whfg unf gb or cynhfvoyr." Fb nsgre n yvggyr qvfphffvba jr pnzr hc jvgu gur vqrn bs gur pneq jvgu gur oraq, uryq syng ntnvafg gur qrpx ol n onyy bs jnk, juvpu riraghnyyl eryrnfrf jura gur jnk tvirf bhg. Jr gevrq vg. Vg qvqa'g jbex. Gur pneq jbhyq ybfr gur oraq. Be gur jnk jbhyqa'g fgvpx. Be vg jbhyq fgvpx gbb jryy. Ohg vg fhvgrq gur fgbel whfg svar. Naq gurer jnf fbzrguvat arng nobhg rira gur gevpx oruvaq gur gevpx orvat zlguvpny.
Yngre, jura jr qrpvqrq gb nqncg gur fubeg fgbel nf n svyz fpevcg, jr jebgr gur gevpx vagb gur fgntr qverpgvbaf, whfg nf gubhtu vg rkvfgrq. Abobql dhrfgvbarq vg. Vg jnf gur cebqhpre'f svefg cebwrpg jvgu hf naq ur nffhzrq jr xarj jung jr jrer qbvat. Vg jnf bayl nsgre jr jrer jryy vagb cer-cebqhpgvba gung jr ernyvmrq gung n pnzren jbhyq unir gb cubgbtencu gur Vaivfvoyr Gernq ebhgvar, v.r., jr'q npghnyyl unir gb qb vg.
Fb jr unq gb purng.
Vs lbh rire frr gur "Vaivfvoyr Guernq" ba ivqrb, jngpu pnershyyl. Lbh'yy abgvpr gung gurer vf n pnzren phg orgjrra gur npgvba bs fubjvat gur orag pneq orvat chg ba gbc bs gur qrpx naq gur zbzrag gung vg cbcf hc. Orgjrra fubgf jr fjvgpurq va n tvzzvpxrq cnpx bs pneqf. Gur gbc pneq jnf ybnqrq hc jvgu orag fcevat fgrry gb tvir vg n tbbq whzc. Gur erfg bs gur cnpx jnf nyy tyhrq gbtrgure va n oybpx naq unq n ubyr qevyyrq guebhtu vg. Gurer jnf n fubeg cvrpr bs svfuyvar gung ena sebz gur zvqqyr bs gur gbc pneq guebhtu gur ubyr va gur cnpx, naq ubbxrq bagb n jver haqre gur erq cnq ba gur pbhagre. gung jver, va ghea, jnf gvrq gb n fgevat, juvpu Craa chyyrq ba phr juvyr ur fnvq uvf yvarf.
Lbh qba'g frr gur svfuyvar naq fgrry ba gur snpr bs gur pneq jura V ubyq vg hc gb Jnyyl orpnhfr, nf V cvpx vg hc, gur pneq qebcf bhg bs ivrj orybj gur ybjre rqtr bs gur gryrivfvba cvpgher vagb gur unaq bs n jnvgvat cebc zna, jub vafgnagyl fhofgvghgrf n cynva orag pneq jvgu n yvggyr jnk va gur zvqqyr.
Yngre jr sbhaq bhg gung fbzr zntvp-fgber bjaref unq pbagnpgrq gurve fhccyvref, vadhvevat jurgure "Vaivfvoyr Guernq, nf Frra Ba GI" jnf ninvynoyr. Jurerire Noare-Pnqnoen Zvyfgrva vf, V org ur'f cebhq.
Va bgure jbeqf, gur pbeerpg nafjre vf gung vg'f vzcbffvoyr naq vg zhfg or fbzr xvaq bs rqvgvat.
In Fake Explanations, Yudkowsky offered a story that has stuck in my mind:
In this story it is also telling that in the many thoughts and explanations that surfaced, the idea "the teacher turned the plate around" was never considered. The students failed to see the correct answer because they weren't thinking creatively enough. While the correct approach in this situation is indeed to notice your confusion, a worthwhile approach still could be to list all the possible solutions you think could be the answer. (And of course only list real solutions that you actually understand, not fake ones.)
So how can we improve this ability to expand our creativity when it comes to considering explanations, so things like "the teacher turned the plate around" enters our list of considerations?
One possible answer: study magic tricks.
In addition to writing and reading stuff on the internet, another hobby I like to indulge in is doing magic tricks with a deck of cards. Many of the tricks I know are very impressive, such as making cards switch places or appearing to read people's minds. However, a lot of the tricks I know are very stunningly simple; some of them don't even involve slight of hand, and could be done by ten-year-olds with little practice. They're just that that cleverly crafted.
I learned a lot of these tricks from YouTube -- many videos will show you a trick and then teach you how it is done. Personally, I don't find the revelation of a trick to take away any of my enjoyment, because I find joy in the merely real, and care little for perpetuating mystery.
However, these YouTube videos for how tricks are done also provide a very effective test for your rationality: watch the trick on the video, and after it is done, pause the video. Spend a good amount of time thinking through the trick, and then finally start thinking through ways you think the trick was done. Only after you have your guesses should you learn how the trick actually was done.
I find that in doing this, I would quickly learn how to think creatively, and found that this not only allowed me to much more effectively figure out how card tricks were done before actually hearing the solutions, but also found that this creativity allowed me to become better at suggesting further hypotheses to other previously confusing situations, as well as becoming better at deliberating to solutions in previously intractable problems.
Not to mention that I managed to learn some rather impressive card tricks.
Good YouTube Magic Lessons: