← Pattern Anatomy

Competition · AMC preparation · step 4 of 4

Pattern Anatomy

Each pattern, deconstructed.

branching-state-enumeration

★ Rank 5/25 5.3% of all AMC problems Grade 2–4

Starting from an initial state, a sequence of choices (each from a small fixed set of actions) generates a tree of reachable states. The question asks for the count of distinct outcomes or valid sequences. Strategy: build the tree level by level, merging duplicate states or pruning states that violate a constraint.

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Sample problem
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amc8-2024-8
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27-year frequency
1999–2026 ↓ 19%
2026 forecast slots
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How to solve

Primary tools organizesee-draw
What to look for
  • Increase step_count from 3 to 4 — tree size grows from 8 to 16 leaves, still listable
  • Add a third action (e.g. +1) to expand the tree without changing strategy
  • Add a 'never go below 0' constraint to convert a state-counting problem into a Dyck-path-flavored one

Sub-archetype mix (5)

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More data (year-over-year, tool fingerprint, grade distribution, all members)
161
members
1999–2026
Active years
Year-over-year

Tool fingerprint (1–17)

Grade distribution

  • Gr 2
    3
  • Gr 3
    3
  • Gr 4
    11
  • Gr 5
    4
  • Gr 6
    8
  • Gr 7
    50
  • Gr 8
    8