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With a shoe that is water proof like an aqua sock you can add Velcro to the entire bottom suface and any towel will stick too it. You can also stick any kind of mopping type rag to it like those new mops have. Any product they make, that can velcro onto those new mops, can be velcroed to your feet. Instead of using all that arm strength in a prone and uncomfortable position you can simply walk and step and slide across the floor even to apply wax to do all kinds of surfaces from wood to linoleum. What would be easier than that?! Nothing. You are simply sliding across a floor and with towels on your feet you wont even slip like you would in shoes when you use a regular mop. You would then be using all your natural weight to clean better than using a little uneven pressure from a stick mop.
Your feet do all the work and the shoes could come in all sizes for men and women and they would last years. You could get these shoes for everyone and it would be fun for all the kids to wear them and mop or wax the floor for you. No more work when the work turns into fun!