These puzzles have no solution

Small Alcazars can be solved with just a bit of intuition, but as you tackle larger levels, the many elegant and complex techniques of the game become more and more relevant.

It's much more fun to find these techniques by yourself than to read about them, so let me simply propose an exercise that may put you on the right path. Here are two Alcazar puzzles. I made the first one, and the second one was created by Edderiofer. Don't try to solve them! They are both impossible. But why? How can you prove that they have no solution?

Leave your questions and hints in the comments! You may use ROT13 ( to hide important clues for those who don't want to see them. I will give a complete explanation in about a week. Have fun!

By the way: the Incredible November sale ends very soon. Make sure to order your copies of the Alcazar book before it ends!

Write a comment

Comments: 17
  • #1

    Leen (Saturday, 22 November 2014 21:12)

    The left one: because it has only black exits. The right one... while I wouldn't know how to even start tackling it, I don't know yet why it doesn't have a solution. I have to think about it!

  • #2

    edderiofer (Monday, 24 November 2014 03:48)

    @Leen, you are incorrect. There is a white exit at the bottom.

    Hint for my puzzle: Svefg, hfr cnevgl gb ryvzvangr nyy gur qnex rkvgf. Gura, qvivqr gur tevq hc vagb avar guerr-ol-guerr ertvbaf. Hfr cnevgl ba rnpu ertvba; fcrpvsvpnyyl zl sbezhyn sbhaq ba zl oybt. Ubj znal gvzrf pna lbh ragre naq rkvg rnpu ertvba? Pna lbh fbzrubj znxr gur ceboyrz fvzcyre, nsgre xabjvat guvf vasbezngvba?

  • #3

    Oderik (Monday, 24 November 2014 09:50)

    @Leen, in addition to edderiofer's comment about the left one: Even if there were only black exits that would not be the point. Think of a level that consists of only one field!

    The main question is quite interesting and distracting - need to focus on other things right now. Reading the hint is tempting, but I'm still trying to resist... ;)

  • #4

    Jérôme Morin-Drouin (Monday, 24 November 2014 10:05)

    The left one has a white exit, indeed, but don't dismiss @Leen's comment too quickly! It's on the right track. Do the 5x7 one first. It's easier, and its trick can be reused for the second one.

  • #5

    jh (Wednesday, 26 November 2014 18:42)

    Gur ynetre chmmyr zhfg unir obgu ragenapr naq rkvg ba n juvgr fdhner, nf orsber; ubjrire gur 4 "ebbzf" va gur fbhgurnfg pbeare, univat na rdhny ahzore bs qnex naq yvtug gvyrf, zhfg unir bccbfvat pbybef. Va cnegvphyne, ng yrnfg bar qnex gvyr zhfg or na rkvg gb guvf frpgvba, ohg gur bayl pnaqvqngrf ner "rkgrevbe" rkvgf ba gur rqtr, pbagenqvpgvat gur birenyy pbafgenvag gung rkgrevbe rkvgf zhfg or juvgr.

  • #6

    Steve (Wednesday, 26 November 2014 19:19)

    whoops, forgot to rot13 that, please delete previous comment!

    Bayl 4 cbffvoyr ynlbhgf cre 3k3 fho nern, guhf fbyhgvba pna bayl ragre/rkvg rnpu 3k3 bapr, naq orpnhfr bs gur yratgu 3 jnyyf gurer'f ab ebhgr sebz OY gb GE gung qbrfa'g ragre gur zvqqyr 3k3 gjvpr?

  • #7

    edderiofer (Wednesday, 26 November 2014 19:28)

    @Steve This is the intended solution, yes.

    @jh This is a far more elegant solution! Great job.

  • #8

    Varanas (Wednesday, 26 November 2014 20:14)

    Thanks for this, working out the solutions has definitely helped me learn a thing or two about alcazar puzzles

    Left puzzle:
    Gurer ner 18 juvgr fdhnerf naq 17 terl fdhnerf. Nf nal cngu jvyy nygreangr juvgr naq terl fdhnerf, gur bayl cbffvoyr fbyhgvba jvyy or bar gung obgu ragref naq rkvgf ba juvgr fdhnerf, ubjrire gurer vf bayl bar juvgr ragenapr.

    Right puzzle:
    Gur fnzr ybtvp pna or nccyvrq gb gur 3k3 frpgvbaf, nal cngu geniryyvat guebhtu n frpgvba zhfg yrnir ba gur fnzr pbybhe gung vg ragrerq ol. Gnxra nf n jubyr, gur cngu zhfg ragre naq rkvg ol juvgr fdhnerf. Nyy juvgr ragenaprf ner va gur pbearef bs gurve 3k3 frpgvba, nf ner nyy pbaarpgvbaf orgjrra 3k3 frpgvbaf. Vs n cngu pna bayl ragre naq rkvg n 3k3 frpgvba ol vgf pbearef, vg pna nyfb bayl ragre naq rkvg bar gvzr rnpu. Vg pna nyfb ragre naq rkvg ol nal pbzovangvba bs pbearef. Xabjvat guvf, jr pna abj fvzcyvsl gur 9k9 chmmyr vagb n 3k3 chmmyr. N 3k3 frpgvba bs gur bevtvany chmmyr vf genafyngrq vagb n fvatyr fdhner va gur arj chmmyr ol cynpvat n jnyy ba n fvqr jvgu ab pbeare rkvgf naq naq na rkvg ba n fvqr jvgu 1 be 2 pbeare rkvgf. Vg vf gevivny gb fubj guvf arj chmmyr unf ab fbyhgvba.

    p.s. I absolutely love the Ball Rooms, they have exactly the difficulty that I wanted and feel has been lacking from most of the rest of the game.

  • #9

    Stefan Franke (Wednesday, 17 December 2014 23:50)

    Gur yrsg bar vf flzzrgevpny. Fb nal fbyhgvba pbhyq or zveeberq naq gurerol pna'g or havdhr?

    Abj yrg'f frr jurgure V pna nccyl guvf gb gur ovttre bar...

  • #10

    Stefan Franke (Friday, 19 December 2014 16:08)

    Oops, stupid argument about the symmetry. Doesn't work..

  • #11

    stan wagon (Thursday, 07 May 2015 02:01)

    I saw these puzzles in Focus. They are easily solved by a function that finds Hamiltonian paths in graphs. Such exist in Mathematica and it took only a tenth of a second to solve the third one in the FOCUS article. My view is that puzzles that cannot be solved by well-known algorithms (dare I say, crossword puzzles) are of much more interest than puzzles that are solvable by computer.

    Stan Wagon

  • #12

    Jérôme Morin-Drouin (Thursday, 07 May 2015 14:26)

    Computers are better than humans at logic puzzles indeed. If you want a challenge that can't be solved in Mathematica, you are on the right page! Look at these these two puzzles, and prove that they have no solution.

  • #13

    stan wagon (Thursday, 06 August 2015 19:27)

    To Morin-Drouin: What you mean "these two puzzles"? The two puzzles given are easily solved by a Hamiltonian algorithm, and I have done so. Were you trying to point me to some other puzzles?

  • #14

    Jérôme Morin-Drouin (Tuesday, 11 August 2015 16:08)

    To Stan Wagon: The two puzzles shown in this blog post have no solution. Here is the proof for the first one:

    The puzzle has 17 black squares and 18 white ones, thus the solution must start and end on white squares (so the solution does: black-white-black-white- ...-black). However, only one of the white squares has an door, meaning that you can either enter or exit the puzzle, but you can't do both.

    I am curious to see what solution you found. Can you give a link or send it to me [jerome at]?

  • #15

    dick (Tuesday, 24 November 2015 00:43)

    Gertyui dfg ah fvbnm FUCK U qwf. Sd bhjcdf.

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  • #17

    witzar (Tuesday, 18 April 2017 15:44)

    Puzzle #2: Qvivqr gur obneq vagb sbhe erpgnatyrf jvgu bar ubevmbagny naq bar iregvpny phgf va fhpu jnl gung hccre-yrsg erpgnatyr vf 3k3. Abj: (1) gur obggbz-yrsg erpgnatyr arrqf gb unir bar juvgr rkvg, (2) gur hccre-evtug erpgnatyr arrqf gb unir bar juvgr rkvg, naq (3) gur obggbz-evtug arrqf gb unir bar oynpx rkvg. Ohg guerr rkvgf vf bar gbb znal.
    Gur bgure jnl gb cebir vg jbhyq or gb ybbx bayl ba gur obggbz-evtug erpgnatyr naq bofreir gung vg arrqf n oynpx rkvg, ohg guvf vf vzcbffvoyr fvapr gur obneqf unf bar juvgr fdhner zber gura oynpx, urapr gur obneq unf gb unir bayl juvgr rkvgf.

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