From New Scientist #1389, 22nd December 1983 [link]
The creature pictured above is a member of the International Eccentric Association of Reindeer. As you see, his particular eccentricity is that he is square, as indeed are the Christmas presents he’s carrying — one for each member of the All-Muggleton XI. Each present is marked with a letter and the edge of each one is a (different) whole number of inches.
Originally the presents were neatly packed around the reindeer’s perimeter so as to fill up the length of each side exactly; furthermore the sum of the areas of the presents on each side was the same.
The packing has become a bit loose, but you can still see which side each present belongs to — although their sizes have been drawn very inaccurately.
To find the side-lengths of the presents (in inches), you need to solve the funny crossword-cum-crossnumber that I have drawn on the reindeer’s side. Here are the clues:
For the key to this ENIGMA, you need to know that not only is the REINDEER square in shape, but if the letters of REINDEER are replaced by certain digits, it becomes a square number. (The square root of “REINDEER” should go, in letters, on the membership card around his neck!). Using the same code, ENIGMA stands for a cubic number whose cube root is double the length of the reindeer’s side.
Finally, on the subject of deer, since it is Christmas I shall give you a present of the fact that “HIND” = 1780.
So — please put the correct 11 numbers in the present squares; the right letters on the neck label; complete the “crossword”; and enjoy a splendid Christmas.
This is the first Enigma of three that were published in the Christmas 1983 issue of New Scientist. It’s also the first Enigma (chronologically) to deviate from the standard numbering scheme.