SOLUTION: There are three triples of positive integers (a,b,c, d,e,f and g,h,i) such that a^2 + b^2 + c^2 = d^2 + e^2+ f^2 = g^2 + h^2 + i^2 = 101. What is the sum of abc + def + ghi?

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Question 1173194: There are three triples of positive integers (a,b,c, d,e,f and g,h,i) such that a^2 + b^2 + c^2 = d^2 + e^2+ f^2 = g^2 + h^2 + i^2 = 101. What is the sum of abc + def + ghi?
Answer by ikleyn(52772) About Me  (Show Source):
You can put this solution on YOUR website!
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Three triples are

(a,b,c) = (1,6,8) :   1^2 + 6^2 + 8^2 = 101


(d,e,f) = (2,4,9) :   2^2 + 4^2 + 9^2 = 101


(g,h,i) = (4,6,7) :   4^2 + 6^2 + 7^2 = 101


Then the sum  abc + def + ghi   is   1*6*8 + 2*4*9 + 4*6*7 = 288.    ANSWER

Solved.