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How many numbers can be expressed as the sum of two or more distinct elements of the set \(\{0, 1, 2, 4, 8, 16, 32, 64, 128\}\)

 Jan 10, 2022
 #1
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The answer is 424.

 Jan 10, 2022
 #2
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This is equivalent to the question "How many numbers can be expressed with 8 or less digits in binary?" 

 

Hence, every number from \(1_2\) to \(11{,}111{,}111_2\) works, for an answer of \(\boxed{255}\)

 Jan 10, 2022

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