A Pretty Basic Problem
On the alien planet Zoop, a classroom of Zoopians are studying different number bases. A student has written in his notes the correct conversion: . Assuming the digits shown represent the same value as digits back on Earth, in what base do Zoopians perform arithmetic?
The answer is 9.
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1 solution
Call the number base in which Zoopians perform arithmetic " x ." We know that the right side of the equation has the value 5 x . The subscript 2 3 on the left side tells us that on planet Zoop, we are working in base 2 x + 3 . Now we can convert 2 3 2 3 to base x as 2 ( 2 x + 3 ) + 3 . Setting this equal to 5 x yields x = 9 .