Go to the right reaching the elevator. Take a look at Clock over the elevator and Control next to it. Rufus will try to put his name as a password but with no success. Examine the Utility Cabinet on the right. Take Soap, Mop and Bucket out of it. Return to the lobby (you can light up the mosaic here too and head to the tower.
Use the Bucket to take some green water from Barrel with Water obtaining Bucket with Water. Put inside it Soap and a Mop getting Mop with Soapy Water.
Return to the Dirty Mosaic Table and use Mop with Soapy Water to clear it. After that action Mop with Soapy Water will break down to Mop Handle and Mop - pick it up. Put the Phosphor Cotton Candy into a Niche under the mosaic and examine it carefully. Rufus will notice that there is a password to the elevator written down on the mosaic but that piece is missing. Use the Chewed Gum on the Mosaic Stone and try to place Mosaic Stone with Chewing Gum into mosaic. Prepare for another mini-game.
Arrange pieces of mosaic as shown on the above screen. It turns out that the last piece doesn't fit at all. Try to push it hard (three times). Unfortunately the mosaic will break down into pieces.