branching-state-enumeration
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.
How to solve
- 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)
Click a row to see member problems.
- markov-state-probability 17% (15)
The process moves through a small set of abstract states labeled by an invariant; the question asks for the probability of hitting or returning to a target state. Solve by writing transition equations or summing a geometric series over the state space.
no figureamc10-2003B-21no figureamc10-2014B-25no figureamc10-2017A-18no figureamc10-2019B-21no figureamc10-2019B-22no figureamc10-2020A-13no figureamc10-2020B-18
amc10-2021A-23no figureamc10-2021B-18no figureamc10-2023A-7no figureamc10-2024A-17no figureamc10-2025B-24no figureamc8-2013-14no figureamc8-2013-8
amc8-2022-25 - constrained-sequence-path 24% (21)
Count sequences or grid paths of fixed length where a structural rule prunes branches at each step (no two consecutive identical elements, must stay non-negative, must return to start); enumerate level-by-level with dynamic programming.
no figureamc10-2005A-18no figureamc10-2006A-25no figureamc10-2006B-17no figureamc10-2008B-22no figureamc10-2012B-22no figureamc10-2015A-10no figureamc10-2015A-22no figureamc10-2015B-20no figureamc10-2018B-6no figureamc10-2019B-25
amc10-2020A-19no figureamc10-2020B-23no figureamc10-2021A-20no figureamc10-2024A-24no figureamc10-2025A-24no figureamc10-2025B-14no figureamc8-2010-25no figureamc8-2013-21
amc8-2017-15
amc8-2020-21
amc8-2024-13 - numeric-operation-tree 18% (16)
A number is transformed by repeatedly applying one of two or three simple operations; the question asks for the count of distinct reachable values after n steps, the minimum steps to reach a target, or all starting values that map to a given output. Grow the forward or backward BFS tree.
no figureamc10-2002A-3no figureamc10-2008A-22no figureamc10-2008B-1no figureamc10-2009A-16no figureamc10-2009B-7no figureamc10-2010A-25no figureamc10-2018B-3no figureamc10-2020A-25no figureamc10-2020B-25no figureamc8-2005-24no figureamc8-2008-12no figureamc8-2019-20no figureamc8-2020-20
amc8-2020-22no figureamc8-2024-8no figuresm-9 - ordered-placement-count 30% (26)
Build an ordered arrangement slot by slot; at each slot the valid choice count decreases because earlier slots constrain later ones (distinctness, adjacency coloring, parity); multiply per-slot choices, splitting by case on the most-constrained slot when needed.
no figureamc10-2002B-9no figureamc10-2004A-12no figureamc10-2005A-9no figureamc10-2006A-18no figureamc10-2007B-20no figureamc10-2008A-23no figureamc10-2008B-21no figureamc10-2009B-11no figureamc10-2010B-23no figureamc10-2011A-13no figureamc10-2011A-22no figureamc10-2012B-11no figureamc10-2013A-24no figureamc10-2014A-4no figureamc10-2015A-18no figureamc10-2017A-19no figureamc10-2018A-4no figureamc10-2018B-18
amc10-2022A-9no figureamc10-2025A-14no figureamc10-2025A-16no figureamc8-2012-10no figureamc8-2015-10no figureamc8-2015-11no figureamc8-2015-4no figureamc8-2017-20 - rule-governed-process-simulation 11% (10)
A cellular automaton, sign-pyramid, game position, or elimination sequence evolves under a local rule for a fixed number of steps; either count starting configurations achieving a target end state (working backward), or simulate forward to identify the resulting state.
More data (year-over-year, tool fingerprint, grade distribution, all members)
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