THE MANDARIN'S "T" PUZZLE.
(
Magic Squares Problem.)
Before Mr. Beauchamp Cholmondely Marjoribanks set out on his tour in the
Far East, he prided himself on his knowledge of magic squares, a subject
that he had made his special hobby; but he soon discovered that he had
never really touched more than the fringe of the subject, and that the
wily Chinee could beat him easily. I present a little problem that one
learned mandarin propounded to our traveller, as depicted on the last
page.
The Chinaman, after remarking that the construction of the ordinary
magic square of twenty-five cells is "too velly muchee easy," asked our
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?
Answer:
There are many different ways of arranging the numbers, and either the 2
or the 3 may be omitted from the "T" enclosure. The arrangement that I
give is a "nasik" square. Out of the total of 28,800 nasik squares of
the fifth order this is the only one (with its one reflection) that
fulfils the "T" condition. This puzzle was suggested to me by Dr. C.
Planck.
[Illustration: THE MANDARIN'S "T" PUZZLE.
+-----+-----+-----+-----+-----+
| | | | | |
| 19 | 23 | 11 | 5 | 7 |
|_____|_____|_____|_____|_____|
| | | | | |
| 1 | 10 | 17 | 24 | 13 |
|_____|_____|_____|_____|_____|
| | | | | |
| 22 | 14 | 3 | 6 | 20 |
|_____|_____|_____|_____|_____|
| | | | | |
| 8 | 16 | 25 | 12 | 4 |
|_____|_____|_____|_____|_____|
| | | | | |
| 15 | 2 | 9 | 18 | 21 |
| | | | | |
+-----+-----+-----+-----+-----+
