lattice-grid-pattern-extrapolation
The literal scale of the problem (thousands by thousands grid, etc.) makes brute enumeration impossible, but the underlying rule is local. Solve the smallest cases by hand on graph paper, look for a pattern (often involving gcd, lcm, or a sum of dimensions), and generalize to the stated size.
풀이 전략
- Change (delta_x, delta_y) from (3000, 5000) to (4000, 6000) — gcd shifts from 1000 to 2000, formula stays the same
- Apply the same dx + dy - gcd pattern to a 'cubes pierced by a diagonal in 3D' variant for harder problems
- Phrase as a 'rectangle cut by a diagonal' problem instead of a segment on graph paper
세부 유형 분포 (5)
한 줄을 클릭하면 그 안의 문제를 볼 수 있어요.
- grid-diagonal-cell-count 5% (4)
Count the cells that a line segment pierces as it crosses a rectangular grid; the formula dx + dy - gcd(dx, dy) is derived by working small cases and noting that each lattice-point crossing avoids a double-count.
- figure-growth-sequence 40% (29)
A geometric figure grows by adding one ring or layer at a time; compute the count for Figure N by identifying the per-layer addition rule from the first 2-3 small figures and applying it to the target N.
no figureamc10-2002A-22no figureamc10-2002B-23
amc10-2003A-23no figureamc10-2008B-7
amc10-2009A-15no figureamc10-2009A-5
amc10-2015A-3
amc10-2018B-8no figureamc10-2024A-6no figureamc10-2025A-19no figureamc10-2025A-5no figureamc10-2025B-3no figureamc12-2006A-23no figureamc12-2008B-24 amc12-2009A-11no figureamc12-2009A-24no figureamc12-2011B-17no figureamc12-2016A-25no figureamc12-2017A-7no figureamc12-2022A-5
amc12-2023A-20no figureamc12-2023A-25no figureamc12-2023B-19
amc8-2002-11
amc8-2004-15
amc8-2009-18
amc8-2013-22no figureamc8-2017-11
amc8-2020-4 - periodic-placement-formula 29% (21)
A large grid, table, or sequence is filled by a short repeating unit of period k; identify the unit cell by examining small cases, compute the count per full period, then add the partial-period tail to reach the answer for the stated large size.
no figureamc10-2004B-19no figureamc10-2012A-14no figureamc10-2013B-13no figureamc10-2014A-24no figureamc10-2018B-20no figureamc10-2024A-20no figureamc12-2002A-21no figureamc12-2004B-12no figureamc12-2007A-24no figureamc12-2012A-24no figureamc12-2013B-7no figureamc12-2014A-23no figureamc12-2015B-20no figureamc12-2015B-25no figureamc12-2018B-18no figureamc12-2021A-16no figureamc12-2022A-18no figureamc12-2025B-24
amc8-2002-23no figureamc8-2007-18
amc8-2023-16 - coordinate-spiral-position 5% (4)
Integers are placed on a grid in a winding or spiral path; locate a specific number or cell by recognizing that layer corners land on perfect squares (or similar landmarks) and counting offsets from the nearest corner.
- lattice-constraint-analysis 21% (15)
Determine which combinations of slope, count, or position are possible for lattice points relative to a line or structured grid by applying number-theoretic constraints such as rational versus irrational slope, GCD divisibility, or AP consistency across rows and columns.
no figureamc10-2011A-25no figureamc10-2011B-24no figureamc10-2016B-14no figureamc10-2021B-25no figureamc10-2024A-21
amc10-2024B-19no figureamc10-2025B-23no figureamc12-2011A-22no figureamc12-2011B-19no figureamc12-2014A-25no figureamc12-2016B-11no figureamc12-2021B-25no figureamc12-2022A-16no figureamc12-2024A-14no figureamc12-2025B-19
더 보기 (연도 추세, 도구 fingerprint, 학년 분포, 전체 문제)
도구 fingerprint (1–17)
학년 분포
- Gr 4 16
- Gr 5 4
- Gr 6 11
- Gr 7 3
- Gr 8 6