Partition marathon · 100 numbers

you send

100 characters of 0 and 1 (which pile each number goes in).

we check

Adds up both piles exactly and measures the gap.

score

log₂ gap, lower wins. 0 means fully solved.

baseline

78.37 · Karmarkar–Karp largest differencing method (1982)

how hard

at this size this is the hardest kind of partition problem

{
  "id": "partition-100",
  "kind": "number-partitioning",
  "seed": "polytime/arena/v1/partition-100",
  "numbers": [
    "814399789462461176249172771771",
    "1100479070572729179439837489394",
    "943927500834847924860015425772",
    "1158142610429169582314168810434",
    "1091337626292833824869426347671",
    "1131551284340908428178165451922",
    "… 94 more"
  ],
  "rule": "Answer bits[i] = 0 or 1 puts numbers[i] in pile 0 or pile 1. Score = log2(|sum(pile 0) - sum(pile 1)|), 0 if the gap is 0 or 1.",
  "answer": {
    "bits": "100 chars of 0/1"
  }
}