Combinatorics Counting List practice with teacher guidance, common slips, and next-step routes.
This skill appears in Systematic list tray build, List missing or duplicate repair, Tree diagram branch read-build, Casework cover board, Place-value property case-count entry, Unique-perfect-matching edge extremum proof, Embedded-graph triangle count with exhaustive witness proof.
Casework cover board asks the player to cover all cases with chips and mark missing, duplicate, or impossible cases.
Word problems are confusing
Embedded-graph triangle count with exhaustive witness proof asks the player to inspect one fixed labeled straight-line graph, enter the total number of valid triangles, and submit the exhaustive set of each triangle's three corner labels.
Word problems are confusing
List missing or duplicate repair asks the player to mark duplicate, missing, or illegal cases in a list.
Word problems are confusing
Place-value property case-count entry asks the player to count values in a finite range that satisfy a digit or place-value predicate and enter the exact cardinality.
Word problems are confusing
Systematic list tray build asks the player to build an organized list of all valid cases using cards or chips.
Word problems are confusing
Tree diagram branch read-build asks the player to read or build branches representing all choices in order.
Word problems are confusing
Unique-perfect-matching edge extremum proof asks the player to for a balanced finite bipartite graph constrained to have a unique perfect matching, submit the maximum edge count, an upper-bound certificate, and an attaining construction.
Word problems are confusing
Fresh independent work can move toward Core, Transfer, or Challenge routes; help use or confusion keeps support visible.
Hints keep attention on the visible structure; reveals show the path without counting as independent evidence.
Presentation can reduce reading and interaction load without changing the selected skill. Practice focus can bias compatible work without breaking prerequisites or story fit.
