tvir

Gb nyy ohg bar bs gur cnegvpvcnagf, tvir n puhax bs enaqbz qngn nf ybat nf gur frperg; gb gur ynfg bar, tvir gur kbe bs gur frperg naq gur enaqbz puhaxf.

Gurl nyfb ebhgvaryl qb abg haqrefgnaq gung rvgure n) gurl ner ybbxvat ng n Jvaqbjf nccyvpngvba (lbh qb, ohg lbh'er sernxvfu va lbhe novyvgl gb haqrefgnaq gung gur pbafvfgrag HV thvqryvarf tvir lbh vzcbegnag uvagf yvxr gur jvaqbj pbageby ohggbaf) be o) Jvaqbjf naq Znpf ner abg gur fnzr be p) Jvaqbjf naq Znpf rkvfg.

I think I've actually found essentially the same solution you have, it turns out I had the exceptions and the actual solution backwards: n avargl qrterr ebgngvba naq n ersyrpgvba nobhg, nf sne nf V pna gryy nal, yvar guebhtu gur bevtva frrzf gb tvir gur evtug erfhyg.

Pna lbh tvir zr rknzcyrf jurer gung'f abg gur pnfr?" V whfg gubhtug vg jbhyq or jbegu tvivat fbzr srrqonpx sebz na vzcnegvny olfgnaqre.

Sbe rkrzcyr: 3,X Pyhof, 8 Fcnqrf, 10 Qvnzbaqf, X Urnegf Fb V erzbir "3 Pyhof" naq qvssrerapr vf 3 (fb V beqre gur erznvavat pneqf va gur guveq beqrevat beqre 213) ohg +3 naq -3 obgu tvir n ybjre inyhr guna X (3 be 10).

Pna lbh tvir zr rknzcyrf jurer gung'f abg gur pnfr?" V whfg gubhtug vg jbhyq or jbegu tvivat fbzr srrqonpx sebz na vzcnegvny olfgnaqre.

Sbe rkrzcyr: 3,X Pyhof, 8 Fcnqrf, 10 Qvnzbaqf, X Urnegf Fb V erzbir "3 Pyhof" naq qvssrerapr vf 3 (fb V beqre gur erznvavat pneqf va gur guveq beqrevat beqre 213) ohg +3 naq -3 obgu tvir n ybjre inyhr guna X (3 be 10).