countryman so to place the numbers 1 to 25 in the square that every
column, every row, and each of the two diagonals should add up 65, with
only prime numbers on the shaded "T." Of course the prime numbers
available are 1, 2, 3, 5, 7, 11, 13, 17, 19, and 23, so you are at
liberty to select any nine of these that will serve your purpose. Can
you construct this curious little magic square?


411.--A MAGIC SQUARE OF COMPOSITES.

As we have just discussed the construction of magic squares with prime
numbers, the following forms an interesting companion problem. Make a
magic square with nine consecutive composite numbers--the smallest
possible.


412.--THE MAGIC KNIGHT'S TOUR.

Here is a problem that has never yet been solved, nor has its
impossibility been demonstrated. Play the knight once to every square of
the chessboard in a complete tour, numbering the squares in the order
visited, so that when completed the square shall be "magic," adding up
to 260 in every column, every row, and each of the two long diagonals. I
shall give the best answer that I have been able to obtain, in which
there is a slight error in the diagonals alone. Can a perfect solution
be found? I am convinced that it cannot, but it is only a "pious
opinion."