This question was proposed in the Scientific American, in 1868: ‘How many revolutions upon its own axis, will a wheel make in rolling once around a fixed wheel of the same size?’

The question brought to the editor of that paper many replies all claiming to have solved it. Yet the replies were about equally divided as to the number of revolutions, one part claiming one revolution and the other two revolutions. So much interest was manifested in it that Munn & Co. published The Wheel, June, 1868. It contains 72 pages, giving many of the solutions, illustrated by many diagrams.

— Miscellaneous Notes and Queries, August 1889

So who’s right?

Three beautiful women and their jealous husbands want to cross a river, but the boat will hold only two people at a time. How can they arrange the crossing if no woman is to remain with a man unless her husband is present?

Take an ordinary chessboard and cut off two diagonally opposite corners. Now: Is it possible to tile the remaining 62 squares with 31 dominoes?

This calls for inspiration rather than trial and error. Most people see the solution immediately or not at all.

White to move. I won’t give the solution — try it out and you’ll see why.

(Composed by V. Röpke, Skakbladet, 1942.)

A chess problem posed by Sam Loyd, published in Le Sphinx, 1866:

“Construct a game which ends with Black delivering discovered checkmate on move four.”

“Christopher Columbus’s Egg Puzzle,” as it appeared in Sam Loyd’s Cyclopedia of Puzzles (1914):

The famous trick-chicken, Americus Vespucius, after whom our great country was named, showed a clever puzzle wherein you are asked to lay nine eggs so as to form the greatest possible number of rows of three-in-line. King Puzzlepate has only succeeded in getting eight rows, as shown in the picture, but Tommy says a smart chicken can do better than that!

Can you?