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  • Directions for question : In this fictitious tale, the two legendary mathematicians and astronomers Aryabhatta and Varahamihira met at a dinner party hosted by King

Directions for question :

In this fictitious tale, the two legendary mathematicians and astronomers Aryabhatta and Varahamihira met at a dinner party hosted by King Chandragupta Vikramaditya at his palace in Pataliputra. 

Aryabhatta, the senior and more moody among the two, being slightly inebriated with the excellent ‘somras’ served by the king, and in a very good mood, suddenly said to Varahamihira -- ‘If distinct alphabets of the english language stand for distinct digits, then SATURN plus URANUS will be equal to JUPITER’!! 

Though initially puzzled by this sudden statement from Aryabhatta, Varahamihira quickly regained composure and solved the challenge thrown by Aryabhatta.

Question :

According to the thought process of Aryabhatta, if (J\alpha )2 = \beta \gamma J, where Jα is a two digit number and \beta \gamma J a three digit number respectively, and \alpha , \beta and \gamma stand for any three of the distinct alphabets used by Aryabhatta (except J), then what would be the crypto form used to express the value of\beta \times \beta \times \gamma?

Option: 1

RAN

 

 


Option: 2

PUT


Option: 3

 JRE

 


Option: 4

TIP 


Answers (1)

best_answer

We already know that the ten letters of the English alphabets Aryabhatta had used in his statement of SATURN + URANUS = JUPITER were in place of the following digits : 

A = 4,

E = 2,

I = 8,

J = 1,

N = 7,

P = 0,

R = 6,

S = 9,

T = 3, and

U = 5

(J\alpha )2 = \beta \gamma J, where Jα is a two digit and\beta \gamma J a three digit number respectively, and α, β and γ stand for any three of the distinct alphabets used by Aryabhatta (except J)

31 is the largest, and 10 is the smallest, two digit number whose square is a three digit number (312 = 961 and 102 = 100)

The tens digit of the two digit number and the units digit of the three digit number is J, that is 1 as per Aryabhatta. Also \alpha ,\beta \text{ and } \gamma are three distinct digits not equal to J, that is 1.

This condition is satisfied only by 192 = 361.

Hence, α, β and γ are having the values of 9, 3 and 6 respectively.

\alpha \times \beta \times \gamma = 9\times3\times6 = 162

Hence, the crypto form used to express the value of \alpha \times \beta \times \gamma is the crypto form used to express the value of 162, that is JRE

 

Posted by

Rishi

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