There are n retailers and each of them have copies of two novels left, titled “FIRST” and “SECOND”. Each retailer has a different number of copies of "FIRST", which is always more than the number of copies of "SECOND" stocked by that retailer.

It is observed that the sum of squares of the number of copies of FIRST and the number of copies of SECOND for each of the retailers is always equal to:
(2²+3²)(3²+4²)(4²+5²).

For example, if the respective number of copies of FIRST and SECOND titles possessed by any given retailer i are x_i and y_i, then :
x_i²+y_i² = (2²+3²)(3²+4²)(4²+5²); for all i = 1,2,....,n

How many retailers are there and how many copies of FIRST novel in total are available from all these (n) retailers?

If each retailer has a distinct number of copies of FIRST and SECOND novels, then the total number of FIRST novels is 612 in stock by the six retailers.

Retailer₁ FIRST= 86 SECOND= 77
Retailer₂ FIRST= 94 SECOND= 67
Retailer₃ FIRST= 98 SECOND= 61
Retailer₄ FIRST=109 SECOND= 38
Retailer₅ FIRST=110 SECOND= 35
Retailer₆ FIRST=115 SECOND= 10

Edited on August 22, 2006, 11:57 am

Posted by Dej Mar on 2006-08-22 11:46:06