Sum of powers of three

I was thinking about sum of powers of three problem (level 5 olympiad). It reads "What is the 50th smallest positive integer that can be written as the sum of distinct powers of 3 with non-negative integer exponents?". Now, if every power in the sum has a distinct exponent then the 50th smallest is a pretty big number [(3**50-1)/2], this is obviously not the answer. If it talks about set of exponents such that {1,1,2} generates 15, {3,0} generates 27, etc. the smallest is 50 as its set is {1,1,1...,1} and every number can be generated this way. I'm quite confused with the wording on this particular problem. :S

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

Discuss the problem afterwards !!! BLOCK THIS POST PLEASE

Shivang Jindal - 8 years, 2 months ago

Sebastian, please avoid posting the problems while the set is live.

Read the question carefully. In particular, pay attention to the word distinct.

Calvin Lin Staff - 8 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$