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MAY, 1892.) ANOTHER INSTALMENT OF THE BOWER MANUSCRIPT.
188
properly made throw of the three dice would, of course, indicate a group of three fields or of the corresponding inscribed figures. Of such groups there would necessarily be three different classes, according as the same number occarred in the group thrice or twice or once; thus the group might be 444, or 443, or 432. It follows that there would be 20 possible groaps, and that every throw of the dioe would indicate one of these 20 groups. Each of these 20 groups or throws is designated by a special name; and the list given below is that of these names.
Further, within each group the numeral figures constituting it may be arranged in different ways; e. g., the group 443 admits of the three variations, 443, 344, 434. Again the group 432 admits of six variations, vix., 432, 423, 342, 243, 234, 324. In fact, every group, containing the same figure twice, admits of three, and every group containing the same figure only once, admits of six variations; while s group, containing the same figare thrice, admits only of one arrangement. Now, there are four possible groups of the latter kind (444, 333, 222, 111); but there are twelve possible groups containing the same figure twice, and four possible groups, eontaining the same figure only once. It follows that the number of possible arrangements or variations of the 20 groups is 64, (i.e., 4 x1 + 12 x 3 + 4 X 6, or 4 + 36 +24).
All this is shown in the First Table below. The groups are arranged in the order in which they would naturally suggest themselves. In the second Table I have given them in the order in which they follow one another in the manuscript; and this order is also shown in the First Table, in the second column, enclosed in brackets. The bracketed numbers in the fourth column give the summations of the figures which compose the several groups.
I.--Table of Groups and Variations.
Classes of Groups,
Serial Number
of Groupa.
Names of Groups
Figures of Groups.
No. of Total No. Total No. of Variations. of Groups. Variations.
With the same figure
thrice.
444 (12) 833 (9) 222 (6) 111 (3) 443 (11) 442 (10) 41 (9)
eo C
c
O
O
With the same figure twice.
Chantayanţa (?)...... IL
Navikki ...............
Pattabandha ......... IV. (IV.) Kalaviddhi ............
(V.) S&pata ............. VI. (XII.) Vrisha .......... VII. (VILI.) Kata ............ VIII. (VI.) MAI ............
(XIV.) Vitf .............
(XVII.) Kana.............. XI. (XIII.) Préshya XII. (XVI.) Saja ................. XIII. (XIX.) Pañicht ............. XIV. (XV.) Karna ...............
XV. (XVIII.) Ohnñchuns ........ XVI. (xx.) Khart XVII. (VII.) Vabula ... XVIII.
(IX.) Bhadri ............. XIX.
(X.) Bakti .................. XX (XI.) Dundubht............
15
12
36
O
O
O
O
113
SOS
O
O
With the same figure
орое.
432 421 () 341 321
O
O
Total..
...
