Counting
21 reasoning problems in this domain. Each starts from a depth archetype and bridges toward a competition type.
Sum of all numbers from digit cards Place-Value Regrouping
Distinct masses weighable with given weights Decompose a Number into Parts and Factors
Log Cutting: Cuts, Pieces, and Time Objects versus Gaps (Fencepost Counting)
Reachable lengths from given bars Length as Sum of Parts with Unit Matching
Length of overlapping strips Overlap Reduces the Total
Count outcomes with a table probability-as-outcome-fraction
Building fractions from number cards equivalent-fractions-scaling
Fractions meeting given conditions inequality-range-membership
Count digits used over a range Repeating Cycle Patterns
Count coin combinations for an amount Decompose a Number into Parts and Factors
List all three-digit numbers from cards enumerate-digit-arrangements
Build values from place-valued items Decompose a Number into Parts and Factors
How often a number appears in the table Decompose a Number into Parts and Factors
Count numbers formed from digit cards Multiplication as Equal Groups
Count outcomes with the multiplication rule Multiplication as Equal Groups
Counting segments, lines, and rays Systematically Count Shapes in a Figure
Count segments joining points on a loop Systematically Count Shapes in a Figure
Trees along a road (fencepost) Objects versus Gaps (Fencepost Counting)
Counting Measurable Lengths count-distinct-combination-sums
Segments joining points on a circle Generalize a Growing Pattern into a Rule
Counting shortest grid paths count-lattice-paths