Methodology docs: per-game aggregation example arithmetic is incorrect

[rbeauchamp]

The ARC-AGI-3 scoring methodology page appears to have an internal arithmetic inconsistency in the per-game aggregation example.

Docs page:

• https://docs.arcprize.org/methodology

Current content:

• Levels 1-3 are described as 0.25 each
• Levels 4-7 are 0
• The formula line then shows (0.25x1 + 0.25x2 + 0.5x3 + 0x4 + 0x5 + 0x6 + 0x7) / (1+2+3+4+5+6+7) = 0.01289 (1.29%)

Why this is inconsistent:

1. The bullet list says the first three level scores are all 0.25, but the formula uses 0.5 for the third weighted term.
2. The stated result 0.01289 matches neither interpretation.

Checked arithmetic:

• If levels 1-3 are all 0.25, then the weighted average is:
  • (0.25*1 + 0.25*2 + 0.25*3) / 28 = 1.5 / 28 = 0.0535714286 (about 5.36%)
• If the intended formula was 0.25, 0.25, 0.5, then:
  • (0.25*1 + 0.25*2 + 0.5*3) / 28 = 2.25 / 28 = 0.0803571429 (about 8.04%)

So the example result should be corrected, and either the bullet list or the formula line should be made consistent with the other.

This looks like a docs/example bug rather than a bug in the scoring rules themselves.

[tianzjyh]

such stupid human who wants to test AI's intelligence !