a locked-room murder (murder in a room locked from the inside)

event, incident / matter, affair / scandal

difficult / hard, probably impossible

hidden room; secret chamber / closed room

untie; unravel; undo (a fastening); unwrap / dispel (doubts); clear up (a matter)

solve (a problem); answer (a question); unravel (a riddle) / comb; untangle (hair)

riddle; enigma

riddle / puzzle / enigma / hint / tip

mystery; puzzle

homicide, especially murder