Assume, Test, and Reject
假设、检验与排除
A strong logic solver does not guess and hope. You make a temporary assumption, follow every consequence, look for a contradiction, and keep only the branches that satisfy every clue.
An assumption is a temporary test branch
Logic becomes manageable when you record one branch at a time instead of holding every possibility in your head.
Warm-up hypothesis laboratory
A mystery number is one of 2, 3, or 4. Both clues must be true: it is greater than 2, and it is even. Test each assumption.
Temporary assumption
Check the reasoning cycle
Separate a contradiction from information not yet known
A contradiction proves a branch impossible. “I do not know yet” only means more clues are needed.
Contradiction
Two required facts cannot both hold in the same branch.
one rank → two studentsone province → two numbered placesexactly one true → two true statementsNot yet known
The branch may still be possible, but the clues have not decided everything.
two choices remaina clue has not been used yeta statement is undecidedA no-tie ranking cannot place two students in one rank.
Two possibilities remain, but neither has broken a rule.
The truth-count rule is broken.
The current branch is unfinished, not automatically false.
Classify each situation
Test the three suspects in the window mystery
This complete practice problem is a friendly first use of the assumption method.
Complete mystery
A classroom window was broken. Only one of three students did it.
Mingming: “Liangliang did it.”
Liangliang: “I did not do it.”
Qiangqiang: “I did not do it.”
Exactly one of these three quoted statements is true. Who broke the window?
Record what each assumption produces
Turn the suspect tests into a proof table
A table prevents a lucky guess from being mistaken for a proof.
| Temporary culprit | Mingming's claim | Liangliang's claim | Qiangqiang's claim | True count | Decision |
|---|
Complete the proof decisions
Add a one-to-one matching rule
The next practice problem matches five numbered locations to five different province labels. No geography knowledge is needed; the province names are simply five distinct labels.
Mini one-to-one matching laboratory
Assign Circle, Star, and Triangle to Lockers 1–3. A valid one-to-one assignment uses every label exactly once.
Complete five-location puzzle
Five numbered locations correspond to five different provinces: Shandong, Hubei, Shaanxi, Jilin, and Gansu. Five students each make two claims.
Rules: each student has exactly one correct claim, and each numbered location is correctly identified by exactly one student.
Student A
1 No. 2 is Shaanxi.
2 No. 5 is Gansu.
Student B
1 No. 2 is Hubei.
2 No. 4 is Shandong.
Student C
1 No. 1 is Shandong.
2 No. 5 is Jilin.
Student D
1 No. 3 is Hubei.
2 No. 4 is Jilin.
Student E
1 No. 2 is Gansu.
2 No. 3 is Shaanxi.
Translate the puzzle rules exactly
Test Student A's first claim and reject the branch
The worked example begins with a clean, definite assumption: suppose A's first claim is correct.
A1 is true:
No. 2 = Shaanxi
E1 says No. 2 is Gansu, so E1 must be false.
E must have exactly one correct claim, so E2 must be true.
E2 gives:
No. 3 = Shaanxi
Shaanxi would occupy No. 2 and No. 3.
Reject A1. Therefore A2 is true:
No. 5 = Gansu
Follow the contradiction chain
Complete the province mapping and audit every clue
Choose one province for each numbered location. The audit panel checks speaker truth counts, number coverage, and duplicate labels.
Your mapping
Study rejected examples (shows worked reasoning)
These examples leave your selectors unchanged. With locations 1–5 set to Shandong, Shaanxi, Shaanxi, Jilin, Gansu, Shaanxi appears twice, breaking the one-to-one rule. With Shandong, Shaanxi, Hubei, Jilin, Gansu, both of Student A’s claims are true, breaking the exactly-one rule.
Live clue audit
Speaker truth counts — each must be 1.
Correct identifications by number — each must be 1.
Submit your complete mapping
The checker evaluates the five selectors above. It does not require a written sentence.
Transfer the method to a new key mystery
This new puzzle is an instructional transfer task. Test each of the three students as the only person who hid the key. Judge the quoted statements, not the students’ personalities.
Complete new mystery
One of three students hid a key.
Ana: “I did not hide it.”
Ben: “I did not hide it.”
Cora: “Ana hid it.”
Exactly one statement is true. Who hid the key?
Prove the answer
Fresh workshop
Try all six fresh checks. Use a hint after your first attempt.
One of Ava, Bo, and Cy hid a badge. Ava says “Bo hid it.” Bo says “Cy hid it.” Cy says “Bo did not hide it.” Exactly one statement is true.
One hint
Test the claims in their written order for each culprit.
Worked reasoning — open after trying
Ava gives F,F,T; Bo gives T,F,F; Cy gives F,T,T. Reject Cy. Ava and Bo both remain possible; the clues do not determine which.
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.
One of Inez, Jo, and Kit moved a book. Inez says “Jo moved it.” Jo says “I did not move it.” Kit says “Inez moved it.” Exactly one statement is true.
One hint
The first two claims are complements. Check whether the third adds another truth.
Worked reasoning — open after trying
Inez gives F,T,T and is rejected. Jo gives T,F,F; Kit gives F,T,F. Jo and Kit survive. Do not claim a unique culprit.
Lesson checkpoints completed
Assumption Detective
You completed the checkpoints on assumptions, contradictions and checking every clue. Revisit any steps for which you needed solution help.
Lesson 10.1 complete
Teaching notes
The mystery-number warm-up, one-to-one locker model, and key mystery are added instructional scaffolds.Province names are used only as distinct labels; students need no geographic knowledge.