Lesson 10.6 — Solve Multi-Attribute Logic Grids and Order Clues
多属性逻辑表与先后顺序线索
Match people to more than one category, connect clues across grids, test a branch when needed, and build only the order facts that the clues truly prove.
Separate the categories before solving
A multi-attribute puzzle can involve the same people in several one-to-one matches. Keep each category separate so that a clue about hats does not become a guess about clothes.
People
These are the objects being matched.
Hat colors
Each hat color is used exactly once.
Clothing colors
Each clothing color is used exactly once.
Use linked logic grids
A grid records one category match. A cross-category clue may require a deduction in a second grid.
Mini demonstration
Kai, Liv, and Mo have different backpack colors and attend different clubs.
- Kai has the green backpack.
- The student with the green backpack attends Art Club.
People × backpack colors
Click a cell to cycle: ? → × → ✓. A ✓ marks the other cells in that row and column as impossible. Conflicting assumptions produce a contradiction message; change or clear those assumptions.
People × clubs
The cross-category clue transfers Kai's confirmed backpack fact into this grid.
Read every clue in the practice problem
A, B, and C each wear one different hat color and one different clothing color. Hat colors and clothing colors are both Red, Yellow, and Blue.
All-different rules: each hat color is used once, and each clothing color is used once.
Direct hat exclusions: A does not wear the red hat. B does not wear the yellow hat.
Hat-to-clothes exclusion: the student wearing the red hat does not wear blue clothes.
Hat-to-clothes confirmation: the student wearing the yellow hat wears red clothes.
Direct clothing exclusion: B does not wear yellow clothes.
A
B
C
Test and reject the branch “A wears the blue hat”
A cannot wear red, so the worked example tests Blue before accepting Yellow. Follow the branch until one person is forced to violate a clue.
Branch state
Force the hat colors with a second branch
A is neither red nor blue, so A must be yellow. The yellow-hat clue then begins a new chain.
Forced-hat state
Complete both grids and audit every clue
Use the linked grids as scratch work, then enter all six final hat and clothing assignments in the dropdowns. The audit checks those dropdowns, not your scratch marks. The checker accepts the result only when every all-different rule and every clue passes.
People × hats
People × clothes
Hat assignments
Clothing assignments
Transfer the method to teachers and subjects
Attributes such as gender or classroom language can eliminate subject assignments even when they are not themselves subjects.
original exercise — three teachers
Teachers A, B, and C teach Chinese, Mathematics, and Foreign Language, one subject each.
- Teacher A uses only Chinese while teaching.
- The Foreign Language teacher is an older brother of one student.
- Teacher C is a woman, and she is livelier than the Mathematics teacher.
Which subject does each teacher teach?
Teacher A
uses only Chinese in class
Teacher B
no direct attribute clue
Teacher C
woman; livelier than Math teacher
Build an order chain without claiming too much
Order clues create arrows such as “Min before Fang.” They may identify the latest person even when the entire four-person order is not unique.
original exercise — who returned latest?
Hong, Fang, Wen, and Min share a dormitory. In this puzzle, each returned once that evening, at a different time, and stayed in the dormitory afterward. Their statements refer to that evening. The person who returned latest forgot to turn off the light. All four statements are true:
- Hong: “When I returned, Wen had not returned yet.”
- Fang: “When I returned, Min was already asleep. Then I went to sleep too.”
- Wen: “When I entered, Fang was already on the bed.”
- Min: “I fell asleep as soon as I returned and did not notice the others.”
Hong returned before Wen.
Min had returned and fallen asleep before Fang returned.
Fang was already on the bed before Wen entered.
Surviving complete orders
| 1st back | 2nd | 3rd | Latest |
|---|
Apply the clues to narrow the 24 possible orders.
Fresh workshop
Try all six fresh checks. Use a hint after your first attempt.
Nia, Omar, and Pia have different badges (Red, Green, Blue) and different clubs (Art, Chess, Music), one of each. Nia has Green. The Green-badge student attends Chess. Omar attends Art and does not have Red.
One hint
Transfer Nia’s badge clue to clubs. Then eliminate colors already used or forbidden.
Worked reasoning — open after trying
Nia is Green/Chess. Omar cannot have Green (used) or Red (forbidden), so Blue/Art. Pia gets Red/Music. Both categories use every value once.
Fresh exit challenge
Complete Missions 2 and 4, this workshop, and all five exit checks to earn your certificate. Reflection and extra exploration are optional.
Four children return at different times. Luz returns before Noor. Milo returns before Noor. Noor returns before Oren. Nothing compares Luz with Milo.
One hint
Combine both arrows into Noor, then the arrow from Noor to Oren.
Worked reasoning — open after trying
Luz/Milo/Noor/Oren and Milo/Luz/Noor/Oren are the two orders. Noor is third, Oren last; Luz and Milo can swap.
Lesson checkpoints completed
Multi-Attribute Logic Architect
You completed the checkpoints on linked grids, cross-category clues and supported order conclusions. Revisit any steps for which you needed solution help.
Teaching notes
The original three-person hat-and-clothing clues, teacher-subject clues, and dormitory-return statements are all restated in English.The linked grids, branch controls, permutation table, audits, transfer explanations, workshop, and exit ticket are added instructional scaffolds.
The dormitory clues determine the latest student but do not uniquely determine all four return positions. The lesson deliberately displays all surviving complete orders so students do not claim more than the clues prove.