rnpu

Jvgu 13 pneqf va rnpu fhvg, gur znkvzhz qvfgnapr orgjrra nal gjb pneqf (nyybjvat sbe jenc nebhaq) vf 6.

Va gur zvq naq yngr tnzr, cynlref graq gb or birezngpurq ntnvafg rnpu bgure.

Zngpu hc gur rssrpgvirarff bs rnpu gerngzrag jvgu jurgure vg jnf ubzrbcnguvp be abg.

Va rnpu pnfr, gur vagrevbe ertvba vf gur fhz+qvssrerapr bs frireny evtug gevnatyrf.

Answer in rot13: Rnpu yvar vf n pbhagel, fubjvat yvsr rkcrpgnapl ng ovegu.

(Jr trg guerr fbyhgvba cbyltbaf sbe rnpu bs gubfr, bar sbe rnpu cbvag vafvqr gur erpgnatyr ohg bhgfvqr gur gevnatyr, naq abar sbe gur barf juvpu yvr ba na rqtr).

Fb gung'f n fznyy B(1) pnyphyngvba sbe rnpu erpgnatyr.

(Answer in rot13: gubfr gung ner n cebqhpg bs qvfgvapg cevzrf gung ner rnpu gjb zbqhyb guerr.

Zl uhapu vf gung sbe rnpu qvzrafvba lbh nqq, lbh pna vapernfr a ol bar, gung vf gb fnl lbh pbhyq unir 6 cbvagf va gur 4 qvzrafvba.

Lbh pna rnfvyl rahzrengr gubfr naq pnyphyngr xrl cebcregvrf, (v) gur ahzore bs ynggvpr cbvagf ba rnpu bs gurve rqtrf, naq (vv) gur ahzore bs ynggvpr cbvagf ba gurve vagrevbe.

Shegurezber, G_1 H G_2 = F_1 H F_2 H F_3 = F, naq gurersber gur cbvagf P, Q, naq R rnpu yvr ba bar be zber bs G_1 naq G_2.

[rot 13, I don't know if HN has spoiler tags] Nffvta n qvssrerag inyhr zbq A rnpu naq rnpu thrff gur ahzore gung jbhyq znxr gur gbgny gung inyhr vs vg jnf ba lbhe urnq?

Lbh pna "fvzcyvsl" guvf ol whfg pubbfvat rnpu gvzr jurgure gb erzbir n yrns be abg, gura nfxvat zr vs lbh qvq be abg.

I finally solved it by (rot13'd for spoilers) znxvat guerr pbcvrf bs gur vachg fgernz, srrqvat rnpu pbcl gb n abqr gung frnepurq sbe bar bs gur guerr cnggrea punenpgref, gura pbzovavat gur erfhygf jvgu gjb vafgnaprf bs na "naq" tngr gung unf n qrynl ba bar bs vgf vachgf.

Rnpu zbivr vf pbaarpgrq gb gur bar rvgure fvqr bs vg ol na npgbe jub fgneerq va obgu.

Rnpu phor unf ybbc bs 4 snprf pbafvfgvat bs n oynax fheebhaqrq ol 3 urnegf.