# Editorial for Lucky Number Seven

Trivial Case 1
$1$ will be represented using $1$ for all base $b \geq 2$.

Trivial Case 2
$2$ is represented as $10$ in base -2. For other bases, it will be $2$.

Hint 1
For base $b \geq X$, the number will be represented as $X$.

Hint 2
For any number $X (>3)$, it can be represented using $1$s in base $b = X - 1$. The representation will be $11$.

Hint 3
It is guaranteed that the number of bits in the lucky numbers will not exceed the number of bits in $N$.

Hint 4
Avoid duplicates (Same numbers represented using only 1s in more than 2 bases).

Solution
Key Idea: For any number$X \geq 3$ can be represented using only 1s in base $2 \leq b < X - 1$, then $X$ will be lucky.
Generate strings of length $3, 4, 5, \dots,$etc. containing only 1s and figure out their values in base-2, 3, … considering the limits discussed above.
All the generated values will be lucky numbers.

### Statistics

63% Solution Ratio

UshanGhoshEarliest, 5M ago

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