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P04 · Geometry

Common-scale consecutive rectangle packing

Pack equally scaled 1×1, 1×2, …, 1×n rectangles into a unit square, maximizing their common scale.

Instancen = 4
ObjectiveMaximize common scale
Requirements
  • Rectangles may rotate by 90°
  • Rectangles neither overlap nor leave the square
  • Every rectangle uses one common scale
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CURRENT LEADERLive answer visualization
n = 4
VERIFIED CONSTRUCTIONscale = 0.100000000
Current leader

0.100000000

common scale

Record holderFounding benchmark
Solution methodHuman only
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Submission format and technical detailsOpen this when you are ready to prepare a JSON certificate＋

Instance parameters

{
  "n": 4,
  "size": 1000000000
}

Current leader certificate

{
  "placements": [
    {
      "rotated": false,
      "x": 0,
      "y": 0
    },
    {
      "rotated": false,
      "x": 100000000,
      "y": 0
    },
    {
      "rotated": false,
      "x": 200000000,
      "y": 0
    },
    {
      "rotated": false,
      "x": 300000000,
      "y": 0
    }
  ],
  "scale": 100000000
}

Submit placements in 1×i order; 90° rotation is allowed. · Verifier v1.0.0