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# Find the one hundredth positive integer that can be written using no digits other than digits 0 and 1 in base 3. Express your answer as a ba

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Find the one hundredth positive integer that can be written using no digits other than digits 0 and 1 in base 3. Express your answer as a base 10 integer.

supermanaccz  May 31, 2018
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Hey superman!

The goal is to count in base 3 using only binary digits.

The $$100^{\text{th}}$$ smallest positive binary integer is $$100 = 1100100_2,$$

so the $$100^{\text{th}}$$ smallest positive integer that can be written with only the binary digits is

$$1100100_3 = \boxed{981}$$.

I hope this helped,

Gavin.

GYanggg  Jun 1, 2018