Indian Antiquary Vol 11

Author(s): Jas Burgess
Publisher: Swati Publications

Page 99

MARCH, 1882.)
THE AMERICAN PUZZLE.
83
THE AMERICAN PUZZLE. BY WM. GOONETILLEKE, HONORARY SECRETARY, KANDY ORIENTAL LIBRARY, CEYLON.
In vol. X. of the Indian Antiquary, page medial vowels, to the first members of sashyogas 89, Mr. George A. Grierson has shewn, by an (conjunct consonants), and to the anusvára. extract from the Jyotistattwa, that the problem Zero is never inserted when it stands alono, but called the "American Puzzle," which, he says, a blank is left in its stead. appeared some months ago in the Pioneer, As Mr. Grierson has given rules for obtain. in a letter headed “From All About," is by ing even totals, I shall only quote from the no means a modern one, dating, as it does, Kakshapuța the mnemonic line for obtaining far book into the history of Indian astrology. both even and odd totals. It is as follows: The problem is to arrange the consecutive
अर्कइन्तुनिधानारी तेन लग्न विनासनं । numbers from one to sixteen in four rows of
Omitting those letters in this line which have four each forming a square, in such a way that the total of every line, and of every possible
no value, viz., final and medial vowels, first
members of conjunct consonants and anusvara, group of four and of the four corner numbers
we get the following 16 letters which exactly will amount to exactly 34. Mr. Grierson has
correspond to the 16 squares, and which are also shewn; what perhaps was not known to the
inserted in them in regular succession, taking American problematists, that any even number
care not to write zero but to leave a blank may be made the total of these lines and groups,
wherever it occurs :in which case, however, the numbers used for filling up the half of the square last filled up
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 will differ. This even number cannot be less | अकादन घन र त न ल न वन सन than 20 in any case, nor can it be less than 34 0108090 2 6 0 3 0 4 0 70 if the same number is not to appear more than The figures below the letters denote their once in the square. But it is not even numbers
value and those above them the numbers of alone that can be obtained as totals. Figures
the squares. can be arranged in the manner already described
By inserting in the squares the values of in such a way that every line and every group these letters as given above, blanks being left of four (except the group consisting of the for 0, we get the following result :fifth, sixth, ninth and tenth squares, and that consisting of the seventh, eighth, eleventh and twelfth squares) and the corner four will amount to any given odd number not less than 21, or not less than 37 if the same number is not to appear more than once in the square. Rules are given in the work called Kekshapuța or Skandhakakshapuța for obtaining both even and odd totals. These consist partly of mnemonic
the remaining eight squares may be filled up verses in which some of the letters represent in such a way as to give even as well as odd figures. The following table shews the value totals. When the total is an even number, of the letters in these verses :
every line and every group of four forming 1 2 3 4 5 6 7 8 9 0 a square and the corner four will amount क ख ग घ च छ ज झ म
to that number as will be seen from the fol
lowing: प फ ब भ म
16 1 13 8 It is the consonants alone that represent the
129 15 2 figures placed above them, the vowel sy being retained for the sake of pronunciation Zero is also represented by the initial vowels TTTT and sit. No values are attached to final or