Math puzzle: The conundrum of sharing

This month, we visit a trendy (but fictional) spa with an unusual feature: hot mud beds.

You lay a plastic sheet on the mud. Then you lay your body upon the sheet. Without any direct contact between mud and body, you spend several minutes enjoying the soft and saunalike heat, sweating all over the plastic. Even though the spa session doesn’t last long, it is said to be wonderfully restorative.

One day, three friends arrive. Unfortunately, only two plastic sheets are available. No one wants to miss out; then again, no one wants to lie on someone else’s sweat.

“Wait!” says one. “It’s simple! I’ll use one side of

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