पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३१३

117

CHAPTER VI--MIXED PROBLEMS.

Vallikā-kuṭṭīkāra.

Hereafter we shall explain the process of calculation known as Vallikā-kuṭṭīkāra^[*]:-

The rule unederlying the process of calculation which is a special kind of division or distribution):-

115${\tfrac {1}{2}}$. Divide the (given) group-number by the (given) divisor; discard the first quotient; then put down one below the other the (various) quotients obtained by the successive division (of the various resulting divisors by the various resulting remainders; again), put down below this the optionally chosen number,

 

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^  It is so called because the method of kuṭṭīkāra. explained in the rule is based upon a creeper-like chain of figures.

115${\tfrac {1}{2}}$. The rule will become clear from the following working of the problem in stanza No. 117${\tfrac {1}{2}}$.

Here it is stated that 68 heaps of plantains together with 7 separate fruits are exactly divisible among 23 persons; it is required to find out the number of fruits in a heap. Here the 63 is called the ‘group-number' and the numerical value of the fruits contained each heap is called the 'group-value' and it is this latter which has to be found out.

Now, according to the rule, we divide first the rāśi, or group-number 63, by the chēda or the divisor 23; and then we continue the process of division as in finding out H.C.F. of two numbers:-

23)63(2      46      ----      17)23(1           17           ----             6)17(2                12                ----                  5)6(1                     5                    ---                     1)5(4                        4                       ----                        1

1 2 1 4

Here, the first quotient 2 is discarded; the other quotients are written down in a line one below the other as in the margin ; then we have to choose such a number as, when multiplied by the last remainder 1, and then combined with 7, (the number of separate fruits given in the problem) will be divisible by the last divisor 1. We accordingly choose 1, which is written down below the last figure in the chain ; and below this chosen number, again, is written down the quotient obtained in the above division with the help of the chosen number. Here we stop the division with the fifth remainder as it is the least remainder in the odd position of order in the series of divisions carried out here.