Compatible task matching

Reassign an alternating chain to cover all tasks without reusing a tool.

Adult planning suggestion: about 9–12 · Logic & rule checking · Cooperation & communication

Players

Groups of 3

Time

12–18 minutes

Materials and quantities

Four fictional task cards A–D, four abstract tool cards X/Y/Z/W, compatibility graph and matching log.

Thirty pupils: ten trios; proposer, mover and checker rotate after the chain is audited.

Prepare

Use the allowed pairs AX, AY, BX, CY, CZ, DZ and DW. A–D and X/Y/Z/W are fictional labels, not pupil names or claims about real equipment. Each task can take at most one tool and each tool can serve at most one task. The printed list is complete; a pair that is not listed is forbidden. Put all cards face up so no social guessing or hidden preference is required.

Play

Try to cover all four tasks. You may undo and reassign earlier legal pairs; a locally available tool is not permanently attached. Record the first trial A–X, C–Y, D–Z, leaving B and W unmatched. B cannot simply take X while A keeps it. To improve the matching, follow a chain of a desired unused edge, an occupied edge back to its task, then another desired edge until a free tool is reached.

Worked example

The chain B–X–A–Y–C–Z–D–W alternates desired and currently occupied edges. Reverse membership along the chain: take B–X, A–Y, C–Z and D–W. All are on the list, and no task or tool repeats. There are now four pairs instead of three. Mark the changed edges before moving cards so an accidental double use of X is visible rather than hidden by rearrangement.

Finish and check

Finish when all four tasks are matched and every edge and uniqueness condition is checked. Four is the maximum here because there are only four tasks and four tools; do not claim the first three-pair attempt is maximal just because B has no immediately free neighbour. The teacher key includes the full chain and final audit. It is not a general algorithm performance test for children.

Adaptation and practical limits

Thirty pupils can work in ten trios as proposer, card mover and edge checker. Adult planning suggestion is roughly 9–12. The university algorithm source is technical background, not a classroom outcome study. Start with the visible three-pair trial and trace by pencil. No one is assigned a public desirability rank, and the task does not ask children to choose or reject real classmates.

Free alternatives: Use paper or clean reused cardboard and a pencil. Copy the supplied diagrams and tables by hand; no specialist kit or purchase is needed.

Printable materials

Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.