Oooh, very nice!
The hints about whether something was solvable were very helpful, in that they made me think harder since I knew I already had all the clues, while not really spoiling any reasoning.
One thing I still can't understand is (rot13) Pynerapr'f "gbqnl jbhyq or yrsg 12 naq evtug 49". Ur vf gnyxvat ba n sevqnl, jr xabj gur arkg zheqre vf ba gur arkg sevqnl, naq nyfb gung gur arkg zheqre vf "gbzbeebj". Nffhzvat gung gur fpenc bs cncre fnlvat gur arkg zheqre jvyy or gbzbeebj unf orra jevggra gbqnl, gura gbqnl vf guhefqnl, naq gur aneengvba gryyf hf gur qngr haybpxrq ol Pynerapr'f uvag vf gbqnl. Ohg jul jbhyq Pynerapr, nyzbfg bar shyy jrrx orsber, ersre gb gur qnl gur aneengbe jbxr hc vzcevfbarq nf "gbqnl" ?