Solution:

MISS SCARLET in the DINING ROOM with the KNIFE

The first guest to go downstairs in search of the scepter was Professor Plum. You can find this out by his forgetful nature when later asked which rooms he searched (which were the Lounge and Conservatory – after taking the secret passage). He had the Lead Pipe, which he later drops.

The second guest was Mrs. White, who hit Plum with her Wrench. She searched the Ball Room and was discovered by the third guest, Mrs. Peacock, who shot her with her revolver. You can deduce this by her remark about Mrs. White’s dastardly language.

Mrs. Peacock moved into the next adjacent room which is the Kitchen. She then took the secret passage between the Kitchen and the Study and was hit in the head by Colonel Mustard and his Candlestick (he is always challenging people to duels).

Mustard searched the Study and Hall, then came across Green and Scarlet searching the Library together. They bumped into each other and exchanged weapons without knowing. Green walked into the Hall and found Mustard, who hit Green with his Candlestick, stealing Green’s new weapon, the Knife (Miss Scarlet had the knife).

Mustard then walked down to the room between the Library and Conservatory – the Billiard Room – and came across Miss Scarlet. She strangled him with Mr. Green’s rope and picked up Colonel Mustard’s Knife, which had been originally hers.

Miss Scarlet then walked into the only unaccounted for room: the Dining Room and found Mr. Boddy, killing him with her Knife.

Luckily Mr. Boddy escaped harm. He woke up after hearing Mrs. Peacock’s gunshots ring through the mansion and raced down to protect his scepter. Miss Scarlet shoved her knife into Mr. Boddy but he was smart enough to be holding his pillow in his arms as well as the scepter, which he used to block the blow. Caught off guard Mr. Boddy fell to the floor in surprise and lost the scepter to Miss Scarlet.

Professor Plum woke up the next morning in a flowerbed with a rather large lump on his head. Mrs. White never got shot by Mrs. Peacock – she dodged the bullet by ducking for cover under the grand piano when she encountered the other woman. She hid there for the rest of the night. Mrs. Peacock and Mr. Green were both knocked out for the night and woke up with nasty headaches. As for Colonel Mustard, he had quite the rope burn on his neck for the next week.

Miss Scarlet never made it off with the scepter. She escaped the Dining Room and ran into the Hall making for the front door but tripped over Mr. Green’s fallen body and fell into a nearby wall. The scepter flew from her hands and crashed into the front door, smashing the scepter to pieces.

Mr. Boddy was about to switch the real scepter with a fake one right when Miss Scarlet found him. She discovered him before he had made the switch and thankfully the real scepter remained in a nearby drawer and stayed safe. Mr. Boddy couldn’t stay made at his guests for too long. By the next day there were all relaxing by the pool outside and the scepter was hauled off to Mr. Boddy’s wing at the museum.