Math Puzzlers

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Certain "puzzlers" in mathematical recreations defy our sense of
experience, leaving you wondering if the answer to a problem can
really be true.

One example is the well-known birthday probability problem, and the
answer that 23 people in a room leads to a 50/50 probability that two
will share the same birthday.

Another is the problem of adding, e.g., "only" one meter to a rope
around the Earth, and determining that the "gap" created between the
lengthened rope and the Earth is about 16 cm. How can it be that
adding such a short length to the rope will result in such a large
gap? Of course,examples on online math forum; it's easy to show using
simple algebra that the result
is a pure value ("amount or rope added"/2pi) independent of any
circumference, so that whether you do it around a superball or around
Jupiter the result will be the same.
Hope the above explanation was useful, now math forum.