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## Number Bases

How would math be different if humans only had 6 fingers and 8 toes? How does a computer do math if it has no fingers to count on?

# Level 1

A $$3$$-digit number has digit sum $$15$$ and is divisible by $$35$$. Find the $$3$$-digit number.

Convert the following number from base 3 to base 9: $\huge{121212121212_3}$

$1111111111111111_{(2)} + 1010101010101010_{(2)} = \ ?$

Clarification: The two numbers given are written in base 2, while the numbers in the answer choices are written in base 16.

True or false:

$$\quad$$ $$\large 0.{111111\ldots}_2 = 1$$.

Find the value of the given equation in base 10 :

$100_2+ 100_{8}+ 100_{10} + 100_{16}$

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