Impossible Escape?
Here's a similar puzzle that can be used as a fun bar trick:<p>Given a standard deck of 52 cards, a third party chooses any five from the deck and hands them to your accomplice. Your accomplice chooses four of the five and gives them to you, with which you identify the fifth card. What's the strategy?<p>Solution (In Rot-13, <a href="http://rot13.com/index.php" rel="nofollow">http://rot13.com/index.php</a>):<p>N fvzcyr beqrevat bs sbhe pneqf qbrfa'g jbex, fvapr 4! bayl nssbeqf lbh 24 pbzovangvbaf (cyhf gur sbhe lbh unir).<p>Jvgu svir pneqf naq bayl sbhe fhvgf, lbh xabj bar bs gur fhvgf zvtug or qhcyvpngrq. Lbh pna hfr gur svefg pneq gb fhccyl bayl fhvg vasbezngvba, ohg gur erznvavat guerr pneqf bayl nssbeq 6 pbzovangvbaf (cyhf 1-4 vs lbh unccra gb qenj pneqf zngpuvat gur gnetrg'f fhvg).<p>Gur frperg vf gb pubbfr juvpu bs gur gjb pneqf gb unaq bire. Jvgu 13 pneqf va rnpu fhvg, gur znkvzhz qvfgnapr orgjrra nal gjb pneqf (nyybjvat sbe jenc nebhaq) vf 6. Ol nterrvat gb nyjnlf unaq bire gur fznyyre/ynetre bs gur gjb pneqf va gur fnzr fhvg nf lbhe fhvg vqragvsvre, lbh pna hfr gur erznvavat guerr gb vaqvpngr gur qvfgnapr hc/qbja sebz gung pneq.<p>Sbe rknzcyr, tvira:
3,5 Pyhof, 8 Fcnqrf, 10 Qvnzbaqf, X Urnegf<p>Qhcyvpngr fhvg vf pyhof, fb jr'yy unaq bire gur fznyyre bs gur gjb (3 Pyhof). Gur qvfgnapr orgjrra 3 naq 5 vf 2, fb jr unaq bire gur gur erznvavat guerr va gur frpbaq ybjrfg beqrevat bs gur pneqf (v.r., 132: 8 Fcnqrf, X Urnegf, 10 Qvnzbaqf).