2020: rgbctf: insert creative algo chall name - 5225225

2020/rgbctf/insert-creative-algo-chall-name/README.md

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+# [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))
+```

2020/rgbctf/insert-creative-algo-chall-name/challenge.txt

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+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.
+
+Example Case:
+Input:
+x = 3
+n = 5
+
+Given the input above we can create a set r that consists of the following n values 
+[2^0, 2^1, 2^2, 2^3, 2^4]
+OR
+[1, 2, 4, 8, 16]
+
+Each combination is formed via x subsets of the set [1, 2, 4, 8, 16]
+[16], [2,8], [1, 4]
+[1, 2, 4], [8], [16]
+[1, 4], [2, 8], [16]
+...
+
+This renders sets of size x that are the sums of the elements of each set
+16, 10, 5
+7, 8, 16
+5, 10, 16
+...
+
+Note: combination 1 and combination 3 are the duplicates and should not be counted twice as they both consist of 5, 10, and 16
+
+All possible unique combinations for x = 3 and n = 5:
+3	8	20
+4	8	19
+1	12	18
+4	9	18
+5	8	18
+2	12	17
+4	10	17
+6	8	17
+1	14	16
+2	13	16
+3	12	16
+4	11	16
+5	10	16
+6	9	16
+7	8	16
+1	2	28
+1	4	26
+2	4	25
+1	6	24
+2	5	24
+3	4	24
+1	8	22
+2	8	21
+1	10	20
+2	9	20
+
+Final Output:
+25 
+(There are 25 combinations generated above)
+
+*IMPORTANT*
+The answer should be formatted as rgbctf{[output value here]} with your output value replacing [output value here]