Tapa (Pentomino) by John Bulten

Tapa by John Bulten


or solve online (using our beta test of Penpa-Edit tools; use tab to shift between shading mode and the composite Yajilin mode where left click marks cells, right click marks dots in cells or X’s on edges, left click+drag draws lines.)

Theme: White Whorl

Author/Opus: This is the 8th puzzle from our contributing puzzlemaster John Bulten.

Rules: Standard Tapa rules. Also, the Tapa wall in this puzzle is made using one of each pentomino given below the grid with no overlaps. Rotations and reflections are allowed. (Note: There is no P pentomino here because it would violate Tapa rules).

Answer String: Enter letters for all pentomino segments from left to right in the marked rows, with one letter for each cell it appears in. Separate each row’s entry with a comma, and use CAPITAL LETTERS.

Time Standards (highlight to view): Grandmaster = 9:00, Master = 13:30, Expert = 27:00

Solution: PDF

Note: Follow this link for other Tapa variations and this link for classic Tapa. If you are new to this puzzle type, here are our easiest Tapa puzzles to get started on.

  • Andrew Brecher says:

    That took a whole lot of trial and error for me. Did I miss a logic path after placing five full pentominos?

    • ghirsch says:

      There was a bit of trial and error, though not a ton. I also got 6 full pentominoes before I had to start guessing a bit, and at that point there wasn’t too much to guess about.

      Znlor lbh zvffrq gur cvrpr va gur gbc evtug pbeare? Gurer ner svir boivbhf funqrq pryyf nebhaq gur fvk pyhr, naq lbh pna fubj gung gurer unf gb or n cragbzvab gung hfrf bayl gur gbc-pragre naq gbc-evtug pryyf, fb ij ner gur bayl bcgvbaf sbe gung pbeare. Gura lbh pna hfr gur gjb-gjb pyhr naq fubj gung gur bayl erznvavat bar-bar pryyf zhfg or orybj gur pyhr, juvpu ybpxf n srj guvatf vagb cynpr. Nsgre gung gurer’f qrsvavgryl fbzr gevny naq reebe, ohg vg’f fvtavsvpnagyl erqhprq, rfcrpvnyyl orpnhfr gurer ner n ahzore bs fcbgf gung bayl unir gjb cbffvoyr bcgvbaf, naq gurer ner n yvzvgrq ahzore bs fcbgf sbe gur k.

      • Andrew Brecher says:

        I don’t see how gur gjb-gjb pyhr sbeprf nalguvat va gur hccre evtug — vf gurer na boivbhf ernfba jul gur V-cvrpr pna’g ynl ngbc gur gjb-gjb? V unq gb gel gur V, cyhf G-I ng gur gbc, orsber V fnj gung gurer jnf ab jnl sbe gur K gb pbaarpg gurz.

        • ghirsch says:

          Vg qbrfa’g qverpgyl sbepr nalguvat, ohg vg’f eryngviryl rnfl gb fubj gung gur V pna’g svg gurer. Gura, orpnhfr bs gur nyernql hfrq cvrprf, nalguvat ryfr gung pna svg nobir gur gjb-gjb (v.r. G/M) zhfg ragre bar bs gur pryyf orybj gur bar-bar, fb gur ynfg fvk pryy unf gb or zvqqyr-evtug, abg zvqqyr-obggbz, juvpu sbeprf gur cvrpr va gur pbeare naq yvzvgf fbzr bgure guvatf.

          I guess I used trial and error in that section, but I’m usually fine with that when it’s the sort of thing where you show in just a few steps that something can’t be true, rather than guessing at large portions of the puzzle and not knowing whether you’re right until the end. It’s definitely possible that there’s an even better method though.

        • Carl W says:

          Andrew, after you helped me see my mistake (further down in the comments) I went back and took another long look at the puzzle from this position.

          V sbhaq n ybtvpny jnl gb ryvzvangr gur V sebz gur cbfvgvba nobir gur gjb-gjb pyhr. Jr xabj gur ybpngvbaf bs svir bs gur fvk erznvavat cragbzvabrf. Naq bayl bar bs gubfr ybpngvbaf (arne gur guerr pyhr) pna or na K. Na V nobir gur gjb-gjb pyhr jbhyq sbepr gur obggbz bs gur chmmyr gb pbaarpg hc guebhtu ebj rvtug pbyhza fvk, (juvpu unf ab ebbz gb orybat gb na K). Fb gur K jbhyq unir gb or ol gur guerr pyhr sbepvat n G orgjrra gur gjb naq fvk pyhrf. Jvgu V naq G obgu fcrag, gur cragbzvab ba gur yrsg jbhyq unir gb or bar bs IJM nal bs juvpu jbhyq pnhfr n gjb-ol-gjb ivbyngvba jvgu gur K. Curj!

          V gevrq n ybg bs bgure ryvzvangvbaf, ohg gung’f gur bayl bar V’ir sbhaq gung qbrfa’g erdhver cynpvat svir cragbzvabf bayl gb svaq gung gur ynfg erznvavat cragbzvab pnaabg fngvfsl pbaarpgvivgl.

        • Andrew Brecher says:

          Thanks, Carl.

  • Rod Bogart says:

    Does the additional rule (Also, the Tapa wall in this puzzle is made using one of each pentomino given below the grid with no overlaps) say that ONLY pentominoes make up the wall? Or that the wall includes all the pentominoes, with some extra cells?

  • John B says:

    Thank you Hirsch for the wrap-up! I’d only add that erzbivat svefg bs vgm ng evtug sbeprf frpbaq bs ij ng gbc, gura mrq onfvpnyyl bayl unf bar fcbg.

  • Carl W says:

    41:42 An excellent challenge, John!

    I didn’t do any guessing, but with 5 full pentominos placed I did stare at the puzzle for an awful long time, (and barely resiisted the urge to start guessing), before making any progress.

    What got me moving again was: V ryvzvangrq V naq G nf bcgvbaf sbe gur cragbzvab fgnegvat sebz gur yrsg fvqr bs ebj fvk, (na V be G gurer jbhyq sbepr gur bccbfvgr pubvpr sbe gur cragbzvab ba gur evtug naq yrnir bayl I sbe gur cragbzvab gb gur yrsg bs gur fvk pyhr naq ab jnl gb fngvfsl gur bar-bar pyhr). Jvgu gubfr gjb ryvzvangrq, guvf cragbzvab zhfg or bar bs IJM zrnavat vg zhfg ernpu gb ebj sbhe, pbyhza sbhe. Jvgu gung pryy xabja, gur bar pyhr va ebj guerr yrnqf dhvpxyl gb n M ba gur yrsg naq gur erfg snyyf vagb cynpr.

    I really liked the ending of this puzzle. (Xabjvat gung K vf n uneq cragbzvab gb svg, V unq orra jngpuvat sbe n cynpr gb svg vg guebhtubhg gur fbyir, ohg sbhaq gung V pbhyq irel eneryl pbafvqre vg nf n cbffvovyvgl sbe nal funqrq pryy sbe irel ybat. V xrcg rkcrpgvat gur chmmyr gb pbafgenva guvatf fb guvf cragbzvab pbhyq bayl yrtnyyl svg va bar cynpr. Fb vg jnf n sha fhecevfr gb cynpr gra cragbzvabf naq svaq gur pragre fgvyy irel bcra jvgu cynprf gung guvf cragbzvab pbhyq fgvyy svg rkprcg gung pbaarpgvivgl sbeprf bar.)

  • Andrew Brecher says:

    Carl – lbh fnl na V be G ba gur yrsg jbhyq sbepr gur bccbfvgr pubvpr sbe gur cragbzvab ba gur evtug, ohg ubj qvq lbh ryvzvangr M nf n cbffvovyvgl ba gur evtug?

    • Carl W says:

      Andrew – Good question! V jnf noyr gb pyvpx “haqb” n mvyyvba gvzrf naq
      frr zl abgrf ng gung cbfvgvba va gur chmmyr. Naq sebz gur orfg V pna
      gryy V fvzcyl zvffrq gur cbffvovyvgl bs n M bire ba gur evtug, (gung
      vf, V jebgr V naq G qbja nf pnaqvqngrf, ohg arire jebgr naq gura
      renfrq M). 🙁 Gunaxf sbe purpxvat zl jbex fb pnershyyl naq pngpuvat
      guvf zvfgnxr, (juvpu raqrq hc whfg orvat n yhpxl zvfgnxr va guvf

  • skynet says:

    30 mins.Tough puzzle

  • Francis says:

    Also took a lot of trial and error for me (mostly error, since I had accidentally “eliminated” the correct arrangement of cells around the 3 clue in the upper left and it took me a while to realize my mistake).

  • egrieg says:

    I have yet to encounter a pentapa i enjoy. This was an absolute torture, i’m sorry to say. After getting stuck i knew that the puzzle was discussediscussed at length in the comments and so i decided to look here for tips, because i knew some trial and error was coming my way. But even after reading all the comments here, even with the deduction about the i pentomino that carl explained and that i never would have found, i still couls not find a logical path. The only reason i kept going was because i had already invested a lot of my time, not because a got even a slight bit of fun out of it. I finally found the solution, but with no uniqueness proven at all, and without an idea how i got to the end. If this puzzle lives up to your grandmaster standards, namely a fair and logical solving path, i would really like to see how on earth it can be found…

  • Avatar photo drsudoku says:

    Gurer jnf fb zhpu ebg-13 rapbqvat gb qb urer V whfg ghearq ba n ohggba gung jbhyq znxr rirelguvat V glcr qb guvf.

    Nsgre gur vavgvny Gncn fgrcf, jvgu fbzr cragbzvab ybtvp, lbh fubhyq or noyr gb cynpr 5 rknpg cragbzvabrf. Gurer vf bar nqqvgvbany gevpxl fgrc, juvpu vf gb frr gung E2P11 zhfg or funqrq. Vs vg vf abg funqrq, gura gurer vf ab jnl gb svyy gur 6 hfvat E2P10 jvgubhg znxvat n H be L (obgu va gur tevq) be ol hfvat E3P9 naq yrnivat na Y hc gbc (nyfb va gur tevq). Bapr E2P11 vf funqrq, lbh pna shegure qrqhpr E3P11 vf funqrq be ryfr na Y be A vf hfrq va gung pbeare (obgu va gur tevq). Gubfr fgrcf trg lbh urer:


    Gurer ner 10 bs gur 11 cragbzvabrf fgnegrq va gur tevq. 6 = VIGJM, 7 = nal, 8 = VIG, 9 = IJ, 10 = VGM, 11 (abg lrg va tevq) = nal.

    Abgr bayl 7 naq 11 pna or K. Ubjrire, gurer vf whfg bar jnl 7 pna or na K naq vg pnhfrf frirer pbaarpgvivgl ceboyrzf vzzrqvngryl. Vs 7 vf K, gura 6 pnaabg gbhpu 7 (vg zhfg or n G), 7 pnaabg gbhpu 8 (vg zhfg or na V) naq gubfr gbtrgure zrna 10 rdhnyf M ohg gura 8 qbrf abg gbhpu 10. Gurer ner sbhe qvfgvapg cragbzvab tebhcf naq gur fvatyr erznvavat pnaabg oevat gurz nyy gbtrgure. Fb 11 vf K.

    Abj, yrg’f rkcyber 10. Vs 10 vf na V, gura gur pbaarpgvba gb gur obggbz cragbzvab tebhc (123) zhfg or guebhtu E8P6, ohg vg hfrf 11 juvpu vf na K naq gung jbhyq sbez n 2k2 fdhner. Fb 10 vf G be M. Guvf abj sbeprf 9 gb or J. Gurer ner rvtug ernfbanoyr pryyf gung gur K=11 pna or pragrerq va. Gur hcqngrq vzntr vf orybj jvgu gubfr 8 pryyf znexrq:


    6 pnaabg or V nf vg jvyy ryvzvangr nyy pryyf sbe gur 11. Fb gur hcqngrq vairagbel vf:
    6 = IGM, 7 = VIGM, 8 = VI, 10 = GM, 11 = K.

    Gur pevgvpny hccre-yrsg 1 pyhr pna abj or pbafvqrerq va E3P3 naq E3P4 (bar bs gurfr vf funqrq). Abgr gung 6 = I jvyy sbepr E3P3 juvpu sbeprf 7 = V juvpu yrnirf ab bcgvba sbe 8. Fb 6 = GM, zrnavat 7 = VI. Gurer ner gjb rvgure/be cnvef 6 naq 10, naq 7 naq 8. Jr pna hfr guvf vasb gb funqr n srj zber pryyf vapyhqvat E456P3. Gur 3 pyhr pnaabg hfr E3P3, fb zhfg hfr E2P5. Orpnhfr gung cragbzvab vf na VI, vg vf abj pyrne vg qbrf abg hfr E3P4 nf jryy. Gur VI rvgure be cnve funqrf E3P67 nygubhtu jr qba’g xabj juvpu fvqr vf gur V be I lrg:


    Abj jr zhfg pbafvqre svany pbaarpgvivgl. Vs 6 vf G naq 10 vf M, gura gur gbc cragbzvab tebhc (789) qbrf abg gbhpu gur obggbz-yrsg be obggbz-evtug tebhc rkprcg guebhtu 11. Ohg gurer vf ab cbfvgvba sbe K gung gbhpurf 6, naq 2/10 ng gur fnzr gvzr. Sbe pbaarpgvivgl, 6 vf M naq 10 vf G.

    Svanyyl, rvgure 6 gbhpurf 7 (zrnavat 7 vf na V) be 6 gbhpurf 11. Gur bayl fcbg sbe 11 gung gbhpurf 6 vf E6P5. Guvf jvyy abg gbhpu 789 gubhtu, abe 2-10. Fb 6 gbhpurf 7. 11 zhfg gbhpu obgu gur gbc cragbzvab tebhc naq gur obggbz-evtug cragbzvab tebhc. Bayl bar cbfvgvba erznvaf sbe gung.

  • egrieg says:

    Wow. Thank you so much for this walkthrough! That must have been a lot of work. It included many steps i would never even have thought of and the images really helped. I learned very much from it, so again a huge thank you!!

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