Anty solutions written

Brilli the Ant says that she has written up ( 100 ) 6 (100)_6 solutions. In decimal notation, how many solutions has she written up?

Details and assumptions

You may choose to read about Number Base Representation .


The answer is 36.

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6 solutions

Prasun Biswas
Dec 20, 2013

( 100 ) 6 = ( 1 × 6 2 + 0 × 6 1 + 0 × 6 0 ) = ( 1 × 36 + 0 + 0 ) = 36 (100)_{6} = (1\times6^{2}+0\times6^{1}+0\times6^{0}) = (1\times36+0+0) = \boxed{36}

Michael Tang
Dec 19, 2013

Haha, this was Level 5 (rating 2900) for a while since the answer was typo'ed :P

Anyway, in decimal notation, 10 0 6 100_6 is written as 1 6 2 + 0 6 + 0 1 = 36 . 1 \cdot 6^2 + 0 \cdot 6 + 0 \cdot 1 = \boxed{36}.

Yes, I was quite surprised that a problem written by the "Best of" section could have a typo. At least now we know how problem ratings work in a sense.

Christian Lee - 7 years, 5 months ago
Gautam Shenoy
Dec 19, 2013

1 × 6 2 + 0 × 6 1 + 0 × 6 0 1 \times 6^2 + 0 \times 6^1 + 0 \times 6^0

Christian Lee
Dec 19, 2013

Using the Number Base Representation as a guide, we know that to convert to our decimal system we can do

( 100 ) 6 = ( 1 × 6 2 ) + ( 0 × 6 1 ) + ( 0 × 6 0 ) = 36 (100)_{6}=(1\times 6^{2})+(0\times 6^{1})+(0\times 6^{0})=36

The answer is 36 . \boxed{36}.

(100)_6 is equivalent to, in base 10,

( 1 × 6 2 ) + ( 0 × 6 1 ) + ( 0 × 6 0 (1 \times 6^2) + (0 \times 6^1) + (0 \times 6^0 )

= ( 1 × 36 ) + 0 + 0 = (1 \times 36) + 0 + 0

= 36 = \boxed{36}

Tanmoy Tk
Jan 13, 2014

1 6^2+0 6^1+0*6^0 =36

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