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How many of the 343 smallest positive integers written in base 7 use 4 or 5 (or both) as a digit?

 Jan 22, 2019
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\(343_{10}=1000_7\)

So the 4 or 5 must be in the 49's, 7's or 1's place.

There are \(49\times 2=98\)\(7\times 2=14\) , and \(1\times 2=2\), so \(98+2+14=114\).

There are 114 of those integers.

 

You are very welcome!

:P 

 Jan 22, 2019

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