Hexadecimals without Letters

Let \(S\) be the set of all real numbers \(r < 1000\) whose hexadecimal (base 16) expansions do not contain any letters (i.e. they only have digits in the set \(\{0, 1, 2, ... 9\}\)).

Find the least upper bound of \(S\).

Details:

For example, \(1.45 \in S\) because its hexadecimal expansion is \(1.7\overline{3}_{16}\), which only consists of the digits \(1,3,7\). However \(240 \not \in S\) because its hexadecimal expansion is \(f0_{16}\) which contains an \("f"\).

Please write the answer in base 10, not 16.

Image credit: Wikipedia
×

Problem Loading...

Note Loading...

Set Loading...