Rank and Match with a Logic Table
Lesson 10.3 · 用逻辑表进行排名与配对
Turn spoken predictions into a one-to-one table, test a branch, use contradictions, and audit every clue before accepting a ranking.
One person per rank. One rank per person.
Build the one-to-one rule
In a no-tie ranking, every person occupies exactly one rank, and every rank belongs to exactly one person.
Try a small logic table
Click a cell to cycle through:
When you confirm one match, the table marks other cells in that row and column as impossible. If you confirm incompatible matches, it reports a contradiction; change or clear the conflicting assumptions.
Check the rule
Translate predictions into a table
Four observers predict the ranks of five Go players A, B, C, D, and E. There are no ties. Each observer has exactly one correct prediction and one incorrect prediction.
| Observer | Prediction 1 | Prediction 2 | Truth quota |
|---|---|---|---|
| Jia | E3rd | A4th | 1 true · 1 false |
| Yi | A3rd | B1st | 1 true · 1 false |
| Bing | B4th | E2nd | 1 true · 1 false |
| Ding | D1st | C3rd | 1 true · 1 false |
| Prediction original | 1st | 2nd | 3rd | 4th | 5th |
|---|---|---|---|---|---|
| Jia | E | A | |||
| Yi | B | A | |||
| Bing | E | B | |||
| Ding | D | C |
Read the table precisely
Test the branch “E is 3rd”
A branch can look reasonable at first. Follow every consequence until it either survives or creates a contradiction.
Rank board
Reveal the assumption first.
Explain why the branch fails
Reject the branch and propagate forced matches
Once “E is 3rd” is rejected, Jia’s other claim becomes true. One forced match creates the next.
Ranking as it becomes forced
Start by rejecting E in 3rd place.
Record the forced matches
Audit the complete ranking
A candidate ranking is not finished until it passes the one-to-one rule and every observer’s exact truth quota.
Enter one player in each rank
Practice with four competitors
The same table method works with a different number of people. Every speaker again has one correct and one incorrect claim.
Complete contest statement
Xiao Zhang: “Xiao Li is 1st; I am 3rd.”
Xiao Wang: “I am 1st; Xiao Zhao is 4th.”
Xiao Li: “Xiao Zhao is 2nd; I am 3rd.”
There are no ties, and each speaker has exactly one correct claim.
Submit the ranking
Find the one wrong prediction—without inventing a full ranking
Sometimes the clues determine only what the question asks. Here, exactly one player’s prediction is wrong, but the middle two ranks are not uniquely fixed.
Predictions
There are no ties. Exactly one complete prediction is wrong. B’s two clauses count together as one prediction: it is true only if B is neither first nor last, and false if either clause fails.
| A | B | C | D |
|---|
Cover every rank
This five-person, no-tie ranking uses a different rule: every rank from first to fifth was guessed correctly by at least one student. It does not say that every student got exactly one claim right.
| Student | Prediction 1 | Prediction 2 |
|---|---|---|
| Zhao | Qian is 3rd | Sun is 5th |
| Qian | Wang is 4th | Li is 5th |
| Sun | Zhao is 1st | Wang is 4th |
| Li | Sun is 1st | Qian is 2nd |
| Wang | Zhao is 2nd | Li is 4th |
Who was predicted for each rank?
Enter the final order
Fresh workshop
Try all six fresh checks. Use a hint after your first attempt.
Ari, Bea, and Cal finish a race with no ties. Ari is not last. Bea finishes before Ari.
One hint
Ari cannot be last, and Bea must have a place before Ari.
Worked reasoning — open after trying
Ari cannot be first because Bea must be earlier. Ari is second, Bea first, Cal third. Check both clues and all three ranks.
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.
Dee, Eli, and Flo finish with no ties. Flo is before Dee and Eli is before Dee. No clue compares Flo and Eli.
One hint
Both other racers must precede Dee. Swap their order to test uniqueness.
Worked reasoning — open after trying
Flo/Eli/Dee and Eli/Flo/Dee both work. Dee is uniquely third; neither earlier rank is fixed.
Lesson checkpoints completed
Logic-Table Ranking Architect
You completed the checkpoints on one-to-one matching, contradictions and checking every clue. Revisit any steps for which you needed solution help.
Teaching notes
Every original puzzle used here is restated in English.The interactive logic tables, branch visualizations, audits, and assessments are added instructional scaffolds.