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# [[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`
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