Brilli the Ant says that she has written up ( 1 0 0 ) 6 solutions. In decimal notation, how many solutions has she written up?
Details and assumptions
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Haha, this was Level 5 (rating 2900) for a while since the answer was typo'ed :P
Anyway, in decimal notation, 1 0 0 6 is written as 1 ⋅ 6 2 + 0 ⋅ 6 + 0 ⋅ 1 = 3 6 .
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.
1 × 6 2 + 0 × 6 1 + 0 × 6 0
Using the Number Base Representation as a guide, we know that to convert to our decimal system we can do
( 1 0 0 ) 6 = ( 1 × 6 2 ) + ( 0 × 6 1 ) + ( 0 × 6 0 ) = 3 6
The answer is 3 6 .
(100)_6 is equivalent to, in base 10,
( 1 × 6 2 ) + ( 0 × 6 1 ) + ( 0 × 6 0 )
= ( 1 × 3 6 ) + 0 + 0
= 3 6
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( 1 0 0 ) 6 = ( 1 × 6 2 + 0 × 6 1 + 0 × 6 0 ) = ( 1 × 3 6 + 0 + 0 ) = 3 6