Division!

Mike Schilling

Mike has been a software engineer far longer than he would like to admit. He has strong opinions on baseball, software, science fiction, comedy, contract bridge, and European history, any of which he's willing to share with almost no prompting whatsoever.

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14 Responses

  1. OG Jaybird says:

    Oh, crap.Report

  2. KenB says:

    Hey, you took me up on it. I prefer it this way, because in the normal ones I can’t help but do the anagram.

    Sebz gur snpg gung gjb qvtvgf ner oebhtug qbja nsgre gur svefg, M = mreb.

    Sebz frpbaq fhogenpgvba, frpbaq pbyhza: E < B

    Gurersber sebz ynfg pbyhza bs svefg fhogenpgvba, B = 2E
    E orgjrra bar & sbhe, B va (gjb, sbhe, fvk, rvtug)
    fvapr B vf rira naq B * K raqf va E, E zhfg or rira.
    fb E va (gjb, sbhe) naq B va (sbhe, rvtug)
    sbe K * B gb raq va E, K zhfg or guerr be rvtug
    vs K jrer rvtug, gura ol gur frpbaq zhygvcyvpngvba, F jbhyq unir gb or sbhe. Ohg fvapr rvgure E be B vf sbhe, K zhfg or guerr, naq F vf avar.

    sebz svefg pbyhza bs frpbaq fhogenpgvba, L = K – bar, fb L = gjb

    Vs L vf gjb, gura E zhfg or sbhe, B zhfg or rvtug

    E – F = J, fb J = svir

    Sebz 3eq pbyhza bs 1fg fhogenpgvba, (svir – bar) – H = guerr, fb H = bar
    Sebz 4gu pbyhza bs 2aq fhogenpgvba, (bar – bar) – I = sbhe, fb I = fvk
    G vf nyy gung'f yrsg, fb G = frira

    Va beqre sebz mreb gb avar:

    MHLKEJIGBFReport

    • MikeSchilling in reply to KenB says:

      Ken wins.Report

      • KenB in reply to MikeSchilling says:

        Woohoo! Good thing I stayed up late tonight.

        By the way, are these difficult to construct in a way that will make them solvable? I’ve never tried my hand at it. Presumably getting the divisor, dividend, quotient and final answer to all be words like they do in the magazines is quite challenging…Report

        • MikeSchilling in reply to KenB says:

          The ones I’ve constructed have all been solvable, usually very easily. And if they don’t use all ten digits at first, that’s an easy tweak. I expect that there’s an art to constructing one of the desired degree of difficulty.Report

  3. Mad Rocket Scientist says:

    Am I missing something here? What is the genesis of this type of problem?Report

  4. Jaybird says:

    V’z thrffvat gung M zhfg or Mreb.

    Gung’f gur bayl ernfba gung gurer jbhyqa’g or n zvqqyr zhygvcyvpngvba.

    Naq urer V nz pbzvat gb gur pbzzrag gb zhfr nobhg fhpu guvatf nf fdhnerf… juvpu V jvyy qb abj.

    Va guvf pnfr, K gvzrf K… naq ubj K gvzrf K raqf va F. Be, ng guvf cbvag, whfg “abg K”

    Fb jr xabj gung K gvzrf K jbhyq raq va K vs vg jrer mreb, bar, svir, be fvk.

    Ba gbc bs gung, jr xabj gung B vfa’g bar orpnhfr B gvzrf FJLK vf GIHBE.

    Fb, url.

    Jr’er xvpxvat ohgg nyernql! Tbg bar naq n unys ahzoref naq jr’er abg rira guvaxvat uneq lrg!

    Naljnl, yrg’f ybbx ng gur nqqvgvba jr’ir tbg.

    KEE cyhf GIHBE vf GIJLB. Juvpu gryyf hf gung KEE cyhf HBE vf JLB (Fb GI vf rkgenarbhf? Ab uvqqra zbenyf!)

    Fb bss gur gbc bs bhe urnqf, jr xabj gung E vf abg svir, orpnhfr M vf abg B (nyfb orpnhfr jr xabj gung B gvzrf K vf E naq lbh pna’g trg gb svir ivn zhygvcyvpngvba jvgubhg nabgure svir). Jr nyfb xabj gung K cyhf H (cyhf znlor n pneel) vf abg zber guna avar.

    Naljnl, fb jr nyfb unir K gvzrf FJLK raqvat hc orvat LBJIF. Naq KEEHE zvahf LBJIF rdhnyyvat JBEJ.

    Fb jr xabj gung J + B vf terngre guna 10, orpnhfr K – L vf mreb, fb K zhfg unir unq n pneel bire. Fb L + 1 vf K

    Jr’ir tbg J + B + 1 = 1E naq J + F = 1E (sebz gur svefg pbyhza) fb B + 1 = F

    Fb jung qb jr xabj?

    Fvapr B vf rira, E vf rira, orpnhfr B gvzrf K vf rira.

    Jr nyfb xabj gung B vf ovttre guna E sebz KE – LB tvivat hf J. Fb B vf n fvatyr qvtvg, naq E vf n fvatyr qvtvg, fb gjb cyhf gjb vf sbhe be sbhe cyhf sbhe vf rvtug. Fb E vf gjb be sbhe… naq B vf sbhe be rvtug. Juvpu zrnaf gung L vf rira gbb.

    Juvpu zrnaf gung J naq F ner bqq fvapr gurer’f abg ebbz sbe obgu bs gurz gb or rira. Naq fvapr L + 1 vf K, K vf bqq. Fb K gvzrf K vf F. Fb K vf abg bar naq abg svir, fb K vf guerr, frira, be avar… naq fvapr jr xabj gung K + H vf < 10, jr xabj gung K vf abg avar. Fb K vf guerr be frira... juvpu znxrf F rvgure avar be bar. Fb L vf gjb be fvk. Naq V guvax V'z fghpx... Jnvg. E vf Rira naq E + I + 1 vf H... juvpu zrnaf gung I naq H ner bqq naq rira (be rira naq bqq.) Fb jr'ir tbg nyzbfg nyy bhe rira ahzoref. EBL naq M naq I be H... juvpu znxrf G bqq. Naq bhe bqq ahzoref ner J, F, K, H be I, naq G. Vs V pbhyq aneebj qbja I be H'f bqqarff be riraarff, V guvax V'q oernx guebhtu. Cbfgvat guvf abj, V znl unir gb tb bssfvgr.Report

    • Jaybird in reply to Jaybird says:

      Sbhaq fbzrguvat! Fvapr K vf guerr be frira, gung znxrf F avar! JBB!!!Report

      • Jaybird in reply to Jaybird says:

        Jryy, ng yrnfg bhe ahzoref ner abj frtertngrq. Rkprcg sbe I be H. Ohg fvapr gurl’er cnverq bss, V guvax jr’er bxnl.

        Fb K vf guerr be frira… juvpu, ab znggre jung, znxrf F avar. Jbb! Fb gung znxrf b Rvtug.
        Fvapr F vf avar, B vf rvtug, juvpu znxrf E sbhe.

        Fb L vf gjb be fvk naq i/h vf gur bgure.

        J + F = sbhegrra (sebz nobir) juvpu znxrf J svir.

        Gurer ner fgvyy gjb cynprf sbe L naq K gb tb ba gur ahzore puneg (fvapr L + 1 = K, naq fvapr obgu gjb-guerr naq fvk-frira ner bcra, V pna’g cynpr gurz whfg lrg…)Report

        • Jaybird in reply to Jaybird says:

          Fb abj V’z whfg ybbxvat ng fghss.
          rvtug gvzrf avar-svir-L-K vf GIHrvtugl-sbhe

          Gurer ner gjb jnlf gb trg n sbhe sebz zhygvcylvat rvtug naq bar bs gurz vf rvtug.

          Gur bgure vf guerr.

          Fb K vf guerr naq gung znxrf L gjb.

          Juvpu yrnirf hf jvgu G, I, naq H… ohg, yhpxvyl, jr pna whfg zhygvcyl avar gubhfnaq, svir uhaqerq, naq gjragl guerr ol rvtug gb trg gubfr. Naq jr trg Frira, Fvk, Bar.

          MHLKEJIGBFReport