small-domain-constrained-search
"선택지가 적을 때 — 그냥 다 시도해보세요"
A finite (often very small) set of candidates is tested against one or more constraints. The natural strategy is to enumerate the candidates — frequently the multiple-choice list itself — and check each against the constraints using guess-and-check or systematic listing.
5개 답안 중 하나 찍기 전에, 3-4번만 case 따져도 충분.
How to solve
- Replace the 1-9 sum with 1-N and seek a different perfect square / triangular number
- Swap two standard dice for one die plus a spinner (1-4) to change the candidate pool
- Increase candidate_set_size modestly so brute enumeration still works but is less trivial
Sub-archetype mix (5)
Click a row to see member problems.
- factor-pair-enumeration 21% (46)
The candidate pool is all integer factor pairs (or ordered triples) of a fixed target product; the solver lists each pair, checks domain constraints such as single-digit, distinct, or ordered, and counts or identifies the valid combinations.
no figureamc10-2019A-14no figureamc10-2019A-6no figureamc10-2019B-14no figureamc10-2019B-5no figureamc10-2020A-11no figureamc10-2020B-7no figureamc10-2021A-11no figureamc10-2021B-17no figureamc10-2021B-5no figureamc10-2022B-13no figureamc10-2023A-10no figureamc10-2024A-7no figureamc10-2024B-6no figureamc8-1999-6
amc8-2000-4no figureamc8-2001-20no figureamc8-2002-6
amc8-2003-15no figureamc8-2003-4no figureamc8-2004-8no figureamc8-2005-6no figureamc8-2006-10
amc8-2006-22no figureamc8-2007-15no figureamc8-2008-15
amc8-2009-12no figureamc8-2009-13no figureamc8-2009-16no figureamc8-2011-8no figureamc8-2012-14no figureamc8-2013-9no figureamc8-2014-23no figureamc8-2014-8no figureamc8-2015-23no figureamc8-2015-8
amc8-2016-6no figureamc8-2017-10no figureamc8-2017-8no figureamc8-2018-13no figureamc8-2019-13
amc8-2020-16
amc8-2022-20no figureamc8-2022-3
amc8-2023-13no figureamc8-2023-25
amc8-2025-22 - sum-target-search 23% (49)
A known total (sum, average, or deficit) pins the problem; the solver enumerates candidates from a small integer range or the given pool — often digits 1–N — and checks which subset sums to the required value, possibly with a secondary constraint such as a perfect-square or distinct-elements condition.
no figureamc10-2019A-12no figureamc10-2019A-4
amc10-2019A-8no figureamc10-2019B-12no figureamc10-2019B-2no figureamc10-2019B-7no figureamc10-2020A-17no figureamc10-2020A-6no figureamc10-2020B-6no figureamc10-2021A-18no figureamc10-2021A-8no figureamc10-2021B-11no figureamc10-2022A-8no figureamc10-2022B-11no figureamc10-2023A-9no figureamc10-2024A-11no figureamc10-2024A-3no figureamc10-2024B-15no figureamc10-2024B-5no figureamc8-1999-3no figureamc8-2000-3no figureamc8-2000-7no figureamc8-2001-4no figureamc8-2002-4
amc8-2003-8no figureamc8-2004-4no figureamc8-2005-8no figureamc8-2006-11
amc8-2007-11no figureamc8-2008-17no figureamc8-2009-23no figureamc8-2010-7no figureamc8-2011-12no figureamc8-2012-18no figureamc8-2012-7no figureamc8-2013-13no figureamc8-2014-12no figureamc8-2015-13no figureamc8-2015-22no figureamc8-2016-11no figureamc8-2016-7no figureamc8-2017-17no figureamc8-2018-14no figureamc8-2020-7
amc8-2022-12no figureamc8-2023-8no figureamc8-2024-12no figureamc8-2024-4no figureamc8-2025-14 - answer-choice-plug-in 18% (39)
Each of the five answer choices is a concrete candidate; the solver tests each one against the stated constraint (which sum is possible, which value satisfies an equation, which arrangement is optimal) and locates the unique match or non-match.
no figureamc10-2019A-3no figureamc10-2019B-4no figureamc10-2020A-5no figureamc10-2020B-4no figureamc10-2021A-14no figureamc10-2021B-1no figureamc10-2022B-7no figureamc10-2023A-4no figureamc10-2023B-2no figureamc10-2024A-4no figureamc10-2024B-3no figureamc8-1999-1no figureamc8-2000-2no figureamc8-2000-5no figureamc8-2001-17no figureamc8-2001-2no figureamc8-2002-2no figureamc8-2003-2no figureamc8-2004-2no figureamc8-2005-5no figureamc8-2006-23no figureamc8-2007-16no figureamc8-2007-19no figureamc8-2008-2no figureamc8-2009-19no figureamc8-2010-6no figureamc8-2011-17no figureamc8-2012-11no figureamc8-2013-1no figureamc8-2014-4no figureamc8-2015-5no figureamc8-2016-5no figureamc8-2017-1no figureamc8-2018-7no figureamc8-2020-6no figureamc8-2022-13
amc8-2023-6no figureamc8-2024-5no figureamc8-2025-6 - factor-divisibility-constraint 17% (36)
The candidate set is determined by divisibility or prime-factorization requirements (common factors, smallest factorial divisible by a given number, greatest prime below a bound); the solver uses factoring or primality to narrow the pool and identify the unique integer meeting all conditions.
no figureamc10-2019A-18no figureamc10-2019A-25no figureamc10-2019A-9no figureamc10-2019B-10no figureamc10-2020A-22no figureamc10-2020B-19no figureamc10-2021A-15no figureamc10-2021B-13no figureamc10-2022B-10no figureamc10-2022B-17no figureamc10-2023B-22no figureamc10-2024A-15no figureamc10-2024A-5no figureamc10-2024B-12no figureamc10-2024B-24
amc8-2000-9no figureamc8-2001-25no figureamc8-2003-12no figureamc8-2004-13no figureamc8-2005-16no figureamc8-2006-24no figureamc8-2009-11no figureamc8-2009-24no figureamc8-2011-21no figureamc8-2012-22no figureamc8-2014-18no figureamc8-2014-2no figureamc8-2015-14no figureamc8-2016-24no figureamc8-2017-23no figureamc8-2020-19
amc8-2022-19no figureamc8-2023-18no figureamc8-2024-15
amc8-2025-24no figuresm-6 - logic-deduction-elimination 21% (46)
The domain is a small structured set — grid cells, logical propositions, or set memberships — and the answer is reached by chaining constraint eliminations (a number cannot appear here because it already appears in that row, a property must hold because it follows by contrapositive) rather than by exhaustive listing.
no figureamc10-2019A-20no figureamc10-2019B-9no figureamc10-2020A-15no figureamc10-2020A-24no figureamc10-2020B-24no figureamc10-2020B-9no figureamc10-2021A-22no figureamc10-2021A-7no figureamc10-2021B-16no figureamc10-2022B-14no figureamc10-2022B-6no figureamc10-2023A-16no figureamc10-2024A-13no figureamc10-2024A-23no figureamc10-2024B-13no figureamc8-1999-15no figureamc8-2000-20no figureamc8-2001-22no figureamc8-2002-17no figureamc8-2003-14
amc8-2003-24no figureamc8-2004-11no figureamc8-2004-17no figureamc8-2005-15
amc8-2006-17no figureamc8-2007-24
amc8-2007-9no figureamc8-2008-22no figureamc8-2009-22no figureamc8-2011-24no figureamc8-2012-16no figureamc8-2013-19no figureamc8-2014-13no figureamc8-2014-21no figureamc8-2015-20no figureamc8-2015-24no figureamc8-2016-20no figureamc8-2017-21no figureamc8-2018-25no figureamc8-2019-19no figureamc8-2020-17no figureamc8-2022-14
amc8-2022-21no figureamc8-2023-14no figureamc8-2023-20no figureamc8-2025-23
More data (year-over-year, tool fingerprint, grade distribution, all members)
Tool fingerprint (1–17)
Grade distribution
- K 1
- Gr 1 2
- Gr 2 2
- Gr 3 11
- Gr 4 54
- Gr 5 17
- Gr 6 74
- Gr 7 24
- Gr 8 30