← Pattern Anatomy

Competition · AMC preparation · step 4 of 4

Pattern Anatomy

Each pattern, deconstructed.

overlap-and-complement-counting

★ Rank 6/25 4.7% of all AMC problems Grade 4–7

Two classifications partition a population (red/white × high-top/low-top) or we want 'at least one' adjacent pair. Direct counting tangles the cases; the trick is either a 2×2 contingency table (inclusion-exclusion) or counting the complementary event and subtracting from 1.

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Sample problem
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amc8-2024-19
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27-year frequency
1999–2026 → 0%
2026 forecast slots
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How to solve

Primary tools organizesee-drawmath-tools
What to look for
  • Change the two fractions in problem 19 (3/5 and 2/3) to (4/7 and 3/4) — table arithmetic changes, structure identical
  • For problem 25 style, change rows × seats from 4×3 to 3×4 or 5×2 — the per-row adjacent count formula updates
  • Try 'maximum red-high-top' instead of minimum to flip the optimization

Sub-archetype mix (6)

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More data (year-over-year, tool fingerprint, grade distribution, all members)
142
members
1999–2026
Active years
Year-over-year

Tool fingerprint (1–17)

Grade distribution

  • Gr 2
    2
  • Gr 3
    1
  • Gr 4
    13
  • Gr 5
    2
  • Gr 6
    13
  • Gr 7
    53
  • Gr 8
    8