Infer a list of numbers from observations of subranges
There's a list of (unknown) integers, in [0...20]. They are generated from a uniform distribution via a RNG.
The input is observations of the form:
* in a subrange [i,j) of the list, and some given threshold T in [0...20], how many sextuples exist (not necessarily of consecutive numbers) consisting of numbers that are less than T.
Example: [0..12), there are 0 sextuples of numbers < 2 This means that for the 12 first numbers of the list, there don't exist 6 numbers which are all less than 2. Another way to view this would be that there exist at least 7 numbers in this range that are >= 2.
Another example: [0..18), there are 1 sextuples of numbers < 7
For the 18 first numbers of the list, there exists one sextuple of numbers that are less than 7 (there could be up to 11 such numbers, but not 12, otherwise there would be two sextuples). Another way to state this would be that, for this range, there exist at least 7 numbers which are >= 7.
Here's an example input, describing known facts about a list of 102 unknown numbers in [0..20] [0..12), there are 0 sextuples of numbers < 2 [0..60), there are 1 sextuples of numbers < 2 [0..18), there are 1 sextuples of numbers < 7 [0..36), there are 2 sextuples of numbers < 7 [0..30), there are 1 sextuples of numbers < 8 [0..36), there are 2 sextuples of numbers < 8 [0..60), there are 3 sextuples of numbers < 8 [0..18), there are 1 sextuples of numbers < 9 [0..42), there are 3 sextuples of numbers < 9 [0..30), there are 2 sextuples of numbers < 10 [0..36), there are 2 sextuples of numbers < 10 [0..60), there are 4 sextuples of numbers < 10 [0..42), there are 4 sextuples of numbers < 13 [0..60), there are 5 sextuples of numbers < 13 [12..72), there are 6 sextuples of numbers < 14 [18..42), there are 1 sextuples of numbers < 10 [18..42), there are 2 sextuples of numbers < 12 [30..60), there are 1 sextuples of numbers < 8 [30..60), there are 2 sextuples of numbers < 11 [36..66), there are 2 sextuples of numbers < 8 [36..66), there are 3 sextuples of numbers < 11 [36..66), there are 3 sextuples of numbers < 12 [42..102), there are 1 sextuples of numbers < 2 [42..102), there are 1 sextuples of numbers < 2 [42..66), there are 1 sextuples of numbers < 7 [42..78), there are 2 sextuples of numbers < 7 [42..102), there are 3 sextuples of numbers < 7 [42..78), there are 2 sextuples of numbers < 8 [42..66), there are 2 sextuples of numbers < 10 [42..72), there are 2 sextuples of numbers < 10 [42..78), there are 3 sextuples of numbers < 10 [42..84), there are 3 sextuples of numbers < 10 [42..102), there are 5 sextuples of numbers < 10 [42..102), there are 6 sextuples of numbers < 13 [60..72), there are 0 sextuples of numbers < 2 [60..78), there are 1 sextuples of numbers < 7 [60..90), there are 2 sextuples of numbers < 8 [60..78), there are 1 sextuples of numbers < 9 [60..90), there are 2 sextuples of numbers < 11 [60..102), there are 4 sextuples of numbers < 11 [60..102), there are 4 sextuples of numbers < 13 [72..102), there are 1 sextuples of numbers < 8 [78..102), there are 1 sextuples of numbers < 10 [78..108), there are 2 sextuples of numbers < 11 [78..102), there are 2 sextuples of numbers < 12 [84.. 945