53.
Here is a prime problem, in more senses than one, which will tax the ingenuity of our solvers:—I am a prime number of three figures. Increased by one-third, ignoring fractions, I become a square number. Transpose my first two figures and increase me by one-third, and again I am a square number. Put my first figure last, and increase me by one-third, and I am another square number. Reverse my three figures, and increase as before by one-third, and for a fourth time I become a square number. What are my original figures?
54.
In how many different ways can six different things be divided between two boys?
55.
What is quite the highest number that can be scored at six card cribbage by the dealer, if he has the power to select all the cards, and to determine the order in which every card shall be played?