Here’s a detailed guide to obtaining a mop in Return to Monkey Island, focusing on the steps involved in solving the puzzle within the kitchen:

Step 1: Talk to the Cook
– Location: Enter the Scumm Bar and proceed to the kitchen located at the far right.
– Action: Interact with the cook by asking him about where to buy a mop. He’ll inform you that you need to either distract him or create your own mop.

Step 2: (Optional) Distract the Cook
– Objective: If you prefer to take the cook’s mop without creating your own, you must distract him.
– Action: The cook is preparing a dish reminiscent of one served at the Governor’s mansion. You will need to know the ingredients of this dish to successfully distract him. However, if you want to skip this distraction entirely, you can proceed to obtain the ingredients book directly.

Step 3: Acquire the Ingredients Book
– Location: Head to the Governor’s mansion, accessible past Low and High street on Mêlée Island.
– Interact with Carla: Look for the “Ingredients” book located on a bookshelf under the stairs. You will need to gain Carla’s forgiveness to borrow the book from her.
– Gift to Carla: Offer her a small gift, such as a frog, to earn her forgiveness. Once she grants it, you can borrow the book.
– Return to the Cook: With the ingredients book in hand, make your way back to the kitchen in the Scumm Bar.

Step 4: Obtain the Mop
– Return to the Kitchen: Present the ingredients book to the cook. This enables you to take his mop.
– Action: Use a knife from your inventory to slice off a piece of the mop’s wooden handle for future use.

Step 5: Create a Map for the Mop-Handle Tree
– Location: Visit Wally’s map store located on Low Street, directly opposite the Voodoo Shop.
– Talk to Wally: Inform him that you need a map to find a tree suitable for crafting a mop.
– Provide the Mop Wood: Hand over the slither of mop wood you took earlier. Wally will use it to create a map.
– Combine Items if Necessary: If you encounter any puzzles needing items, such as combining two monocles for a makeshift tool, handle them as they arise, although this may not be essential just for the map.

Step 6: Locate the Mop-Handle Tree
– Use the Map: Follow the directions indicated on the map provided by Wally to find the mop-handle tree.
– Action: Once you reach the designated location, you will be able to collect the materials needed to create your own mop.

Conclusion
This guide presents you with two potential approaches for obtaining a mop: either by distracting the cook or by creating one from the ground up. Each method requires careful navigation through the game’s environment and interaction with various characters, enhancing your gameplay experience in Return to Monkey Island.

For further tips and variations specific to your difficulty setting (Casual or Hard), consider consulting detailed walkthroughs tailored to those modes.