Vs lbh xabj nyy gur nafjref gura lbh pna qrgrezvar gur cnffpbqr. Vs rvgure bs uvagf 2 be 3 ner "ab", gur nafjref gb gur uvagf jbhyq abg havdhryl pbafgenva gur ynfg qvtvg, naq gurer jbhyq or zhygvcyr cbffvoyr fbyhgvbaf.
Vs uvagf 2, 3 naq 5 ner "lrf", lbh pna nyernql qrqhpr nyy sbhe qvtvgf! Lbh'ir tbg k23l, lbh xabj l > k+2+3, naq *gur chmmyr gryyf lbh gurer vf bayl bar fbyhgvba*. Fb k+2+3 pnaabg or yrff guna 8, be gurer jvyy or zhygvcyr cbffvovyvgvrf sbe l, naq vg pnaabg or zber guna 8, be gurer jvyy or ab cbffvovyvgvrf sbe l.
> Vs rvgure bs uvagf 2 be 3 ner "ab", gur nafjref gb gur uvagf jbhyq abg havdhryl pbafgenva gur ynfg qvtvg, naq gurer jbhyq or zhygvcyr cbffvoyr fbyhgvbaf.
Naq, ntnva, gur chmmyr gryyf lbh gung jba'g unccra! Fb lbh pna nffhzr gung gur bayl jnl gur nafjref qb pbafgenva nyy gur qvtvgf vf vs gur fhz bs gur svefg guerr qvtvgf vf 8, naq gura obgu lrf/ab naq ab/lrf sbe uvagf 2 naq 3 tvir lbh rknpgyl bar fbyhgvba.
Gur rkcrpgrq fbyhgvba gnxrf nqinagntr bs guvf fnzr ybtvp: nafjref "ab, lrf, lrf, ab" gb gur svefg sbhe dhrfgvbaf yrnir cbffvovyvgvrf bs 3, 5 naq 7 sbe gur svefg qvtvg. Gur bayl ernfba lbh pna cvpx bar vf gung gur inyhr unf gb pbafgenva gur ynfg qvtvg. Ohg gur fnzr vf gehr vs lbh'ir bayl nafjrerq "lrf, lrf" gb uvagf 2 naq 3: gur svefg qvtvg pbhyq or nalguvat, ohg bayl bar inyhr jbexf.
Lbh pna guvax bs guvf nf n evqqyr jurer 2 cresrpg ybtvpvnaf jvgu qvssrerag vasbezngvbaf gnyx gb rnpu bgure ol bayl fnlvat fghss yvxr "v qba'g xabj gur nafjre" naq "ng svefg v qvqa'g xabj gur nafjre, ohg abj gung lbh gbyq zr lbh qvqa'g xabj gur nafjre, v xabj gur nafjre"
-Qenxarx pubbfrf n cnffpbqr.
-Qenxarx tvirf gur 5 uvagf naq gurve nafjref gb Nyvpr.
-Qenxarx tvirf gur 5 uvagf jvgubhg gurve nafjref gb Obo.
-Nyvpr gryyf Obo gung fur xabjf gur cnffpbqr, naq gung vs bar bs gur 5 uvagf jrer erzbirq fur jbhyqa'g xabj vg
-Lbh'er Obo, lbh unir gb svaq gur cnffpbqr
Abj ubj gb fbyir vg:
-Jvgu lbhe xabjyrqtr gung ab uvagf ner erqhaqnag, Obo pna qrqhpr gung obgu uvagf 1 naq 4 zhfg or nafjrerq ol n Ab; Qvtvg 1 = 3,5,7 be 9
-Jvgu lbhe xabjyrqtr gung Nyvpr xabjf gur cnffpbqr, Obo pna qrqhpr gung uvag 5 zhfg or nafjrerq ol n Lrf, bgurejvfr gurer jbhyq or jnl gbb zhpu cbffvovyvgvrf
-Abj vf gur cneg v guvax lbh zvffrq, vs sbe rknzcyr Uvag 2 jnf nafjrerq ol n Ab, gura Nyvpr jbhyqa'g xabj gur cnffpbqr sebz gur trg tb (sbe nyy fur xabjf vg pbhyq or nal pbqr orgjrra 3037, 3038, 3039, 3138, 3139 be 5039). Gur snpg gung fur xabjf gur cnffpbqr sebz gur uvagf nybar yrgf Obo qrqhpr gung Uvag 2 vf nafjrerq ol n Lrf.
-Gur fnzr ybtvp pna or qbar sbe Uvag 3. Abj Obo xabjf gur nafjref gb nyy 5 Uvagf (ALLAL), naq pna rnfvyl svaq gung 3239 vf gur bayl cbffvoyr cnffpbqr
Jung V guvax lbh'er zvffvat sebz zl nethzrag vf gung fvapr uvag 5 vf gur bayl cvrpr bs vasbezngvba jr unir nobhg gur sbhegu qvtvg, jr pna xabj, jvgubhg pbafvqrevat gur bgure dhrfgvbaf ng nyy, gung gur sbhegu qvtvg zhfg or 9 naq gur fhz bs gur bgure guerr zhfg or 8. Bgurejvfr gur chmmyr vf hafbyirnoyr. Fvapr jr ner cebzvfrq gung gur chmmyr vf fbyirnoyr, jr pna znxr guvf qrqhpgvba, naq nafjrevat "ab" gb uvag 2 be "ab" gb uvag 3 rnpu tvir hf rknpgyl bar fbyhgvba (naq nafjrevat "lrf" gb obgu znxrf dhrfgvbaf 1 naq 4 erqhaqnag).
Lbhe Nyvpr naq Obo fvghngvba qbrfa'g zveebe bhef rknpgyl: Nyvpr qbrfa'g xabj gur ceboyrz vf fbyirnoyr! Naq Obo xabjf fur qbrfa'g xabj guvf, naq gung gurersber fur fbyirq vg jvgubhg gur qrqhpgvba nobir. Va gung pnfr, gurer vf vaqrrq bayl bar fbyhgvba, gur rkcrpgrq bar. Ohg jr qb xabj gur chmmyr vf fbyirnoyr, naq gung punatrf gur vasbezngvba ninvynoyr gb hf naq gur cbffvoyr fbyhgvbaf. Hasbeghangryl, fvapr gjb fbyhgvbaf erznva, gur chmmyr raqf hc frys-pbagenqvpgbel.
Lbhe Nyvpr naq Obo fvghngvba qbrfa'g zveebe bhef rknpgyl: Nyvpr qbrfa'g xabj gur ceboyrz vf fbyirnoyr! Naq Obo xabjf fur qbrfa'g xabj guvf, naq gung gurersber fur fbyirq vg jvgubhg gur qrqhpgvba nobir. Va gung pnfr, gurer vf vaqrrq bayl bar fbyhgvba, gur rkcrpgrq bar. Ohg jr qb xabj gur chmmyr vf fbyirnoyr, naq gung punatrf gur vasbezngvba ninvynoyr gb hf naq gur cbffvoyr fbyhgvbaf. Hasbeghangryl, fvapr gjb fbyhgvbaf erznva, gur chmmyr raqf hc frys-pbagenqvpgbel.
"V erzrzore gung vs lbh xabj nyy gur nafjref gura lbh pna qrgrezvar gur cnffpbqr" vf jung znxrf gur nyvpr/obo fvghngvba zveebe guvf chmmyr rknpgyl
Nyvpr qbrfa'g xabj nalguvat nobhg gur chmmyr jr'er gelvat gb fbyir, ohg jr'er gbyq gung fur pna svther bhg gur cnffpbqr ol bayl hfvat gur 5 uvagf naq nafjref, juvpu jbhyqa'g jbex jvgu uvagf 2 be 3 orvat nafjrerq ol n ab
njvrzm, I've been enjoying the discussion here, and I've just written a little solver for this puzzle. Now I'm curious if you consider this updated puzzle broken as well:
I've forgotten my 4 digit passcode!
Fortunately, I saved some hints on my phone. All the hints have a yes/no answer. I remember that if you know all the answers then you can determine the passcode.
The hints are:
- Is the first digit smaller than the second digit?
- Is the second digit smaller than the third digit?
- Is the third digit smaller than 4?
- Is the first digit even?
- Is the fourth digit smaller than the sum of the first two digits?
Unfortunately, to access the answers to the hints, I need to log in to my phone with my passcode :(
(Notes: There's no information about redundancy of the hints. Also, this puzzle has a unique solution)