Step 1: Materials
waxed or parchment paper
hand towel or rags
small flexible putty knife
Step 2: Arrange dry ice
Tear off a piece of waxed paper or parchment paper large enough to cover a tile and overhang an inch or two on each side.
While wearing insulating gloves, arrange the chunks of dry ice on top of the paper to cover the offending tile. Cover the ice with a towel or two to insulate it.
Wait 2-3 minutes. Read a book, like I did. Often, you can hear an audible "pop" when the tile comes loose.
Step 3: Repeat
Use the piece of paper, pulling on the edge, to reposition the dry ice to the next, more offensive, tile.
Use the scraper or putty knife to lift the previous tile. Often, you can just lift the tile up with your fingertips. Put the tile in a bag or box. If left on the floor, it will soon re-adhere itself.
Step 4: Repeat until the floor is clean
If you aren't bored enough, attack what little adhesive remains after a tile removal with the putty knife, while it is still cold.