At the beginning of the story, Green has the Wrench, Peacock has the Rope, Scarlet the Candlestick, Plum the Pipe, and Mustard the Revolver and Knife. Mustard is placed in Bedroom 1, Plum in 2, Scarlet 3, Peacock 4, Green 5. Peacock and Scarlet switch rooms, so that Scarlet is in Bedroom 4 and Peacock in 3. Mrs. Peacock leaves the Rope in room 3, thereby leaving her weaponless.
When the other guests are in the Lounge before dinner, Peacock steals the Knife out of Mustard's room. Green and Plum switch bedrooms, and White and Mustard switch bedrooms, so that Green is in Bedroom 2, Plum 5, Mustard 6, and White 1;
Mrs. White takes possession of the Revolver that Mustard forgets when he switches bedrooms with her. Since Ms. Scarlet is killed with a non-blunt weapon,
it must be with Peacock's Knife, because the only other non-blunt weapons are the Revolver and the Rope. Ms. Scarlet has possession of the Rope, and Professor Plum has the Revolver,
but forgets he has before going to sleep and he has no apparent motive to kill Ms. Scarlet.
Scarlet is murdered in her own bedroom, so she must be killed in BEDROOM #4.
The motive is clear. Ms. Scarlet`s and Mr. Green`s relatives had a successful enterprise running in the 1930s, and Petunia Peacock, with the help of the Boddys,
stole it from them. In retaliation, the Greens burned down the original Boddy Beach House, and the Scarlets murdered Petunia Peacock. Mrs. Peacock murdered Ms. Scarlet out of revenge. Unfortunately for Mrs. Peacock, she doesn't actually kill Ms. Scarlet; in the dark, she stabs one of Ms. Scarlet's pillows, not realizing that Ms. Scarlet had passed out on the floor (where Mrs. White finds her the following morning) from drinking too much champagne.