# [[2017-03-06] Challenge #305 [Easy] Permutation base](https://www.reddit.com/r/dailyprogrammer/comments/5xu7sz/20170306_challenge_305_easy_permutation_base/)

There may be an actual name to this base system (let us/me know in comments),
and there is a math insight that makes this problem even easier, but it is
still pretty easy with no math insight.

For *permutation base 2*, the indexes and values start with:

| index | value |
| :---: | ----: |
|   0   |    0  |
|   1   |    1  |
|   2   |   00  |
|   3   |   01  |
|   4   |   10  |
|   5   |   11  |
|   6   |  000  |
|   7   |  001  |
|   8   |  010  |
|   9   |  011  |

## Sample challenge

What is the base-value for index `54`?

What is the index-value for base `111000111`?

## Example

    permbase2 54
    1 1 0 0 0

    permbase2 inv 1 1 1 0 0 0 1 1 1
    965

## Challenge index inputs (some are 64-bit+ inputs)

    234234234
    234234234234234
    234234234234234234234234

## Challenge value inputs

    000111000111111000111111000111111000111
    11111111000111000111111000111111000111111000111

## Bonus

Extend the function to work with any base. Base 10 index value `10` is `00`.
Index value `109` is `99`