This month, we visit a modern (but imaginary) resort with an unusual feature: hot clay family.
You put a plastic sheet on the mud. Then put your body on the paper. Without any direct contact between clay and body, you spend a few minutes to enjoy soft heat and rug, and sweating throughout the plastic. Although the spa session does not last long, it was said that it is a wonderful thiyami.
One day, three friends arrive. Unfortunately, only two plastic sheets are available. No one wants to miss. Then again, no one wants to lie on another person’s race.
“I am waiting!” One says. “It’s simple! I will use one aspect of the paper, and you can use the other.”
“are you kidding?” Other responses. “This side will be covered with mud.”
The first friend smiles. “Not if we plan for the future.”
#1: How can all three friends participate in the spa using only two papers?
#2: The next day, five friends visit the spa, and only three leaves are available. Can they all participate? (Let’s assume that the spa is now prohibited from placing the side of falling from a sheet directly on their precious clay.)
#3: Soon, 10 friends visit the spa. Only five sheets are available. “Someone will have to miss,” one of them will declare. Another says: “There is no way to know that, so we look at least for a solution.” Who is the correct?
#4: Later, the spa presents a second type of clay, which should not be mixed with the first. If three friends want to try both clay, how many papers they need at least? (Suppose every person is very ready to lie twice on the same paper.)
#5: The launching here is a completely general question, which is something that sports researchers have not yet been: What is the minimum number of papers that allow friends to experience species of clay if each side may touch only one person or a kind of mud? (You may start assuming M = 1.)
While trying these puzzles, I recommend seizing some index cards or paper leaves to manipulate them. Or if you feel ambitious, move to some plastic leaves, and some friends smell of sweat and correct comfortable clay.
Looking for answers? Go to Sciencenews.org/puzzle- Netwers. We would like to hear your thoughts. Send us to email our correspondent Buzzles@sciencenews.org.
