Pattern & rule

36 reasoning problems in this domain. Each starts from a depth archetype and bridges toward a competition type.

Old multiplication methods Apply a Newly Defined Operation → Branching State Enumeration

Finding the hidden rule Generalize a Growing Pattern into a Rule → Lattice / Grid Pattern from Small Cases

Find missing numbers in a skip-count rule Generalize a Growing Pattern into a Rule → Lattice / Grid Pattern from Small Cases

Read positional rod numerals Place-Value Regrouping → Arithmetic Expression Decomposition

Represent numbers by figure rule Generalize a Growing Pattern into a Rule → Lattice / Grid Pattern from Small Cases

Simplify long sums using regularity Sum of Evenly Spaced Numbers via the Middle → Arithmetic Expression Decomposition

Convert ancient symbol numerals Apply a Newly Defined Operation → Arithmetic Expression Decomposition

Broken clock with constant drift Track a Quantity Through Changes → Arithmetic Expression Decomposition

Find the rule in a fraction sequence Generalize a Growing Pattern into a Rule → Lattice / Grid Pattern from Small Cases

Sum shaded numbers in an array Sum of Evenly Spaced Numbers via the Middle → Lattice / Grid Pattern from Small Cases

Train timetables and elapsed time Elapsed Time and Base-Sixty Regrouping → Arithmetic Expression Decomposition

Weekday of a date from the 7-day cycle Repeating Cycle Patterns → Modular Cycle Frequency Count

Shrinking self-similar shapes Generalize a Growing Pattern into a Rule → Geometric Series Share

Finding equivalent fractions equivalent-fractions-scaling → Multiplicative Ratio with Integrality Constraints

Count stones at a given step of a growing pattern Generalize a Growing Pattern into a Rule → Lattice / Grid Pattern from Small Cases

Find numbers placed by an arrangement rule Generalize a Growing Pattern into a Rule → Lattice / Grid Pattern from Small Cases

Find the missing or nth shape in a pattern Repeating Cycle Patterns → Lattice / Grid Pattern from Small Cases

Analogical reasoning with figure pairs analogy-transfer-relation → Small-Domain Constrained Search

Find the rule for a growing figure Generalize a Growing Pattern into a Rule → Lattice / Grid Pattern from Small Cases

Discover the hidden operation rule Apply a Newly Defined Operation → Arithmetic Expression Decomposition

Find a fraction in a patterned sequence Generalize a Growing Pattern into a Rule → Lattice / Grid Pattern from Small Cases

Decode the shape-to-number rule Apply a Newly Defined Operation → Arithmetic Expression Decomposition

Sum of a rectangle in a number grid Sum of Evenly Spaced Numbers via the Middle → Lattice / Grid Pattern from Small Cases

Sum of consecutive odds and evens Generalize a Growing Pattern into a Rule → Arithmetic Expression Decomposition

Sum of consecutive numbers by pairing Sum of Evenly Spaced Numbers via the Middle → Pair-Sum Invariant

Complete the multiplication table Solve a Table or Graph Step by Step from Clues → Small-Domain Constrained Search

Units-digit pattern of each times table Repeating Cycle Patterns → Units-Digit Tracking

Find cells from a window-sum rule Solve a Table or Graph Step by Step from Clues → Lattice / Grid Pattern from Small Cases

Apply a newly defined symbol rule Apply a Newly Defined Operation → Arithmetic Expression Decomposition

Finding the day of the week Repeating Cycle Patterns → Modular Cycle Frequency Count

Division applications challenge Repeating Cycle Patterns → Modular Cycle Frequency Count

Sequences and units-digit cycles Repeating Cycle Patterns → Units-Digit Tracking

Lengths in an Arithmetic Progression Generalize a Growing Pattern into a Rule → Lattice / Grid Pattern from Small Cases

Diameter and radius in nested circles Radius and Diameter Relationships → Path Length Comparison & Shortest Path

Clock chimes and hand cycles Repeating Cycle Patterns → Modular Cycle Frequency Count

Equivalent fractions from a diagram equivalent-fractions-scaling → Multiplicative Ratio with Integrality Constraints