Some of them are waste!

Algebra Level 5

$a^2+b^2+c^2+d^2+e^2+f^2=139$ $a^3+b^3+c^3+d^3+e^3+f^3=783$ $a^2+b^2+c^2+d^3+e^3+f^3=551$ $a^3+b^3+c^3+d^2+e^2+f^2=371$ $a^2+b^3+c^2+d^3+e^2+f^3=499$ $a+b+c+d+e+f=?$ Hint: This set

The answer is 27.

1 solution

Akhil Bansal
Sep 6, 2015

$\text{Your hint worked}$
$\text{I arbitarary finded the sum of square}$ $\text{of first 7 natural numbers and then observed that}$
$1^2+2^2+3^2+4^2+5^2+6^2+7^2 = 140$

$\text{Subtracting first term i.e 1}$ , $\text{which becomes equivent to given expression}$ .
$\textit{ a=2,b=3,c=4,d=5,e=6,f=7}$ .
Hence, $\textit{ 2+3+4+5+6+7 }= 27$

Well... it is a useless hint.

Adam Phúc Nguyễn - 5 years, 9 months ago

What other ways are there other than guessing?

Also, is this solution unique? It might not be.

Calvin Lin Staff - 5 years, 9 months ago

Some of them are waste!

The answer is 27.

1 solution

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