We classify the algebraic phenomena of a particular family of wreath products that can be viewed as coming from the family of puzzles about switches in the corners of rotating tables. Such puzzles have been written and popularized since they were first popularized by Martin Gardner in 1979. Classify large families of garland products according to whether they correspond to solvable puzzles, classify puzzles perfectly if switches behave like the Abelian group, and classify all garland products that are $p$ groups. Build a winning strategy. It provides novel examples of other puzzles in which switches behave like non-Abelian groups, such as those consisting of two interchangeable copies of the monster group $M$. Finally, we offer some open questions and speculations, and offer other suggestions on how some of these ideas can be generalized further.