# [insert creative algo chall name]

writeup by [5225225](https://www.5snb.club) for [BLÅHAJ](https://blahaj.awoo.systems)

**Misc**
**449 points**
**67 solves**

> Find the total number of unique combinations for input values of x = 4 and n = 12
>
> There exists a set of values, r, with values binary increasing (2^0, 2^1, ... 2^(n-1))
>
> A combination is a set of x values where each value is generated by creating x subsets of r with
> all values within a subset being summed
>
> The x subsets should use all values in r exactly once.

(full challenge text in challenge.txt)

## Writeup

This is fairly simple stuff, easily translated into python. I installed more-itertools
(<https://more-itertools.readthedocs.io/en/stable/)> for `set_partitions`, which makes this problem
trivial.

```python
import more_itertools

x = 4
n = 12

r = [2**i for i in range(n)]

parts = more_itertools.set_partitions(r, k = x)

summed = []
for p in parts:
    o = set()
    for i in p:
        o.add(sum(i))
    summed.append(o)

print(len(summed))
```