Leave the tavern and proceed to Bellevue. Click on the red pathway (left from the entrance to Doc's workshop). Along the way, pick up the fifth puzzle fragment (on the counter of the booth found on the right side of the scene). Use the bowl of peanuts on the scanner (fine nose) at the gate. Enter the house on your right and talk to the captain.
Proceed to the left side of the area and click on the first door on the left (Old City). Talk to the Platypus Trapper - you'll learn that to enter the elite Platypus Club, you need to get a membership card hidden in a Chinese fortune cookie. Approach the window on your left and use the bell. Ask for a takeout. You'll be left with a restaurant menu - three menus to choose from with extra options. Choose menu nr.2 (for 3, 0 c) and point the mouse to the hamburgers so that both are marked. Change two small hamburgers for one bigger, then switch up the large burger for a large soda. Change the large soda for the smallest one, and do the same with a medium one. Change two smallest sodas for two burgers, and exchange two burgers to one large. Exchange the large burger for a large soda, change large soda into a small one, and finally, change the small soda into nothing. The only thing left on the tray will be a free fortune cookie. Give it to the fisherman in the docks - you'll receive a membership card.
Give the membership card to the Platypus Trapper - he will give you a guide. Read it - you'll learn that there are four types of platypus - guardians of the nest, representing four elements. Click on the platypus eggs and their small ones to get the needed information. Before you leave the area, pick up the sixth puzzle fragment (the saltshaker at the restaurant table).