An algebra problem by Luiz Ponce Alonso Ponce

Algebra Level 3

a>b>c>d>e>f>g>0 are integers such that 10^6 = 2^a +2^b +2^c +2^d +2^e +2^f +2^g The value of sqrt ( 1 +a +b+c+d+e+f+g ) is

9 7 10 8

1 solution

Ricardo Alencar
Feb 28, 2015

As we need a number with only $2^i$ elements, without repetition and $i > 0$ , we are looking for the binary representation of $10^6$ Therefore: $(10^6)_{10} = (1111\ 0100\ 0010\ 0100\ 0000)_2$

Leading us to the following values of $a,b,c,d,e,f,g$ :

$19, 18, 17, 16, 14, 9, 6$

Hence: $\sqrt{1 + 19 + 18 + 17 + 16 + 14 + 9 + 6} = \sqrt{100} = 10$

An algebra problem by Luiz Ponce Alonso Ponce

1 solution

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