This is a bit of a work in progress. I'm only going through the steps to clear the level, to get the diary pieces, and because of the math puzzle. (There are extra things you can do. I don't know if they're necessary.)
Save at the beginning to ensure you get all four diary pages for this level.
Start room. There should be diary in this room.
Go up right, get Popcorn. There should be diary in this room.
Down, give popcorn to corn guy, turns on lights.
Go upstairs again, get Axe. Get Knight and Puzzle Piece from cabinet. Get Spray Bottle.
Go down, then left. Use the Axe on the middle poster. Take the "E".
Go right, use the E on the machine.
There are several possible solutions to this puzzle, depending on the numbers you have. They must equal 24. You may use fractions.
1 2 3 9 => 9 x 3 - 2 - 1
2 2 2 3 => 2 x 2 x 2 x 3
3 6 6 8 => 3 x 8 + 6 - 6
4 4 7 7 => 7 x (4 - 4 / 7) [Use the division sign.)
5 5 5 1 => 5 x (5 - 1 / 5) [Use the division sign.)
5 7 7 8 => 8 + 8 x (7 - 5)
7 8 8 9 => 8 + 8 x (9 - 7)
Get the smiley ticket. Give it to the corn guy. Get the Star.
Go left. Use the Star. Go left.
You're in the theater. There should be a diary in this room.
Press Reel 1 and watch. Pick up the "I" Puzzle Piece at the left.
Go up to VIP. Give the Knight to the man.
On the top right there are four circles.
The answer is Teal, Red, Blue, Yellow (or, by clicks, 5, 2, 4, 6).
Go right. There should be diary in this room.
At this point you shouldn't have to solve more puzzles except the exit puzzle.
The solution is Red Bishop, Blue Knight, Blue King, Red Pawn.
Go through the door.