Understand the logic behind multi-person logic puzzles practice
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Worksheet 2 of 10 (11% complete)
Question 1
Logic puzzle:
You meet two people. A says: 'At least one of us is a knave.' B says nothing.
What are A, B, and C (or A and B)?
If A knave → statement 'at least one knave' true → but knave can't tell truth → impossible. So A knight → statement true → at least one knave → since A knight, B must be knave.
Question 2
Logic puzzle:
Three people, A, B, and C, are each either a knight (always tells truth) or knave (always lies).
A says: 'B is a knave.'
B says: 'A and C are the same type.'
C says: 'A is a knight.'
What are A, B, and C (or A and B)?
Case analysis: If A knight → B knave (A's truth) → A and C different (B's lie) → C knight? But C says 'A is knight' which would be true, consistent. Wait, need full check.
Actually solve: Assume A knight → 'B knave' true → B knave → B's statement 'A and C same' is false → A and C different → C knave → C says 'A knight' which is false (since A knight?) Contradiction.
Therefore A knave → 'B knave' false → B knight → B's statement true → A and C same → C knave → C says 'A knight' false (since A knave) ✓. Solution: A knave, B knight, C knave.
Question 3
Logic puzzle:
Three people, A, B, and C, are each either a knight (always tells truth) or knave (always lies).
A says: 'B is a knave.'
B says: 'A and C are the same type.'
C says: 'A is a knight.'
What are A, B, and C (or A and B)?
Case analysis: If A knight → B knave (A's truth) → A and C different (B's lie) → C knight? But C says 'A is knight' which would be true, consistent. Wait, need full check.
Actually solve: Assume A knight → 'B knave' true → B knave → B's statement 'A and C same' is false → A and C different → C knave → C says 'A knight' which is false (since A knight?) Contradiction.
Therefore A knave → 'B knave' false → B knight → B's statement true → A and C same → C knave → C says 'A knight' false (since A knave) ✓. Solution: A knave, B knight, C knave.
Question 4
Logic puzzle:
You meet two people. A says: 'At least one of us is a knave.' B says nothing.
What are A, B, and C (or A and B)?
If A knave → statement 'at least one knave' true → but knave can't tell truth → impossible. So A knight → statement true → at least one knave → since A knight, B must be knave.
Question 5
Logic puzzle:
A says: 'I am a knight or B is a knave.' B says: 'A is a knave.'
What are A, B, and C (or A and B)?
Test cases: - A knight → statement true: 'knight or B knave' → true (first part true) ✓. B says 'A knave' which is false, so B knave ✓. - A knave → statement false: 'knight or B knave' false → both parts false → 'knight' false (ok), 'B knave' false → B knight. Then B says 'A knave' which would be true (since A knave), but B knight must tell truth ✓. This also works? Wait, if A knave and B knight: A's statement 'knight or B knave' = 'false or false' = false (knave lies) ✓. B's statement 'A knave' = true (knight truth) ✓. Two solutions? But puzzle assumes unique. Check carefully: With A knave, B knight: A says 'knight or B knave' = 'false or false' = false (good lie). B says 'A knave' = true (good truth). Both work. So puzzle ambiguous. We'll take first solution: A knight, B knave.
Question 6
Logic puzzle:
A says: 'I am a knight or B is a knave.' B says: 'A is a knave.'
What are A, B, and C (or A and B)?
Test cases: - A knight → statement true: 'knight or B knave' → true (first part true) ✓. B says 'A knave' which is false, so B knave ✓. - A knave → statement false: 'knight or B knave' false → both parts false → 'knight' false (ok), 'B knave' false → B knight. Then B says 'A knave' which would be true (since A knave), but B knight must tell truth ✓. This also works? Wait, if A knave and B knight: A's statement 'knight or B knave' = 'false or false' = false (knave lies) ✓. B's statement 'A knave' = true (knight truth) ✓. Two solutions? But puzzle assumes unique. Check carefully: With A knave, B knight: A says 'knight or B knave' = 'false or false' = false (good lie). B says 'A knave' = true (good truth). Both work. So puzzle ambiguous. We'll take first solution: A knight, B knave.
Question 7
Logic puzzle:
You meet two people. A says: 'At least one of us is a knave.' B says nothing.
What are A, B, and C (or A and B)?
If A knave → statement 'at least one knave' true → but knave can't tell truth → impossible. So A knight → statement true → at least one knave → since A knight, B must be knave.
Question 8
Logic puzzle:
You meet two people. A says: 'At least one of us is a knave.' B says nothing.
What are A, B, and C (or A and B)?
If A knave → statement 'at least one knave' true → but knave can't tell truth → impossible. So A knight → statement true → at least one knave → since A knight, B must be knave.
Question 9
Logic puzzle:
Three people, A, B, and C, are each either a knight (always tells truth) or knave (always lies).
A says: 'B is a knave.'
B says: 'A and C are the same type.'
C says: 'A is a knight.'
What are A, B, and C (or A and B)?
Case analysis: If A knight → B knave (A's truth) → A and C different (B's lie) → C knight? But C says 'A is knight' which would be true, consistent. Wait, need full check.
Actually solve: Assume A knight → 'B knave' true → B knave → B's statement 'A and C same' is false → A and C different → C knave → C says 'A knight' which is false (since A knight?) Contradiction.
Therefore A knave → 'B knave' false → B knight → B's statement true → A and C same → C knave → C says 'A knight' false (since A knave) ✓. Solution: A knave, B knight, C knave.
Question 10
Logic puzzle:
Three people, A, B, and C, are each either a knight (always tells truth) or knave (always lies).
A says: 'B is a knave.'
B says: 'A and C are the same type.'
C says: 'A is a knight.'
What are A, B, and C (or A and B)?
Case analysis: If A knight → B knave (A's truth) → A and C different (B's lie) → C knight? But C says 'A is knight' which would be true, consistent. Wait, need full check.
Actually solve: Assume A knight → 'B knave' true → B knave → B's statement 'A and C same' is false → A and C different → C knave → C says 'A knight' which is false (since A knight?) Contradiction.
Therefore A knave → 'B knave' false → B knight → B's statement true → A and C same → C knave → C says 'A knight' false (since A knave) ✓. Solution: A knave, B knight, C knave.
Question 11
Logic puzzle:
A says: 'I am a knight or B is a knave.' B says: 'A is a knave.'
What are A, B, and C (or A and B)?
Test cases: - A knight → statement true: 'knight or B knave' → true (first part true) ✓. B says 'A knave' which is false, so B knave ✓. - A knave → statement false: 'knight or B knave' false → both parts false → 'knight' false (ok), 'B knave' false → B knight. Then B says 'A knave' which would be true (since A knave), but B knight must tell truth ✓. This also works? Wait, if A knave and B knight: A's statement 'knight or B knave' = 'false or false' = false (knave lies) ✓. B's statement 'A knave' = true (knight truth) ✓. Two solutions? But puzzle assumes unique. Check carefully: With A knave, B knight: A says 'knight or B knave' = 'false or false' = false (good lie). B says 'A knave' = true (good truth). Both work. So puzzle ambiguous. We'll take first solution: A knight, B knave.
Question 12
Logic puzzle:
You meet two people. A says: 'At least one of us is a knave.' B says nothing.
What are A, B, and C (or A and B)?
If A knave → statement 'at least one knave' true → but knave can't tell truth → impossible. So A knight → statement true → at least one knave → since A knight, B must be knave.
Question 13
Logic puzzle:
A says: 'I am a knight or B is a knave.' B says: 'A is a knave.'
What are A, B, and C (or A and B)?
Test cases: - A knight → statement true: 'knight or B knave' → true (first part true) ✓. B says 'A knave' which is false, so B knave ✓. - A knave → statement false: 'knight or B knave' false → both parts false → 'knight' false (ok), 'B knave' false → B knight. Then B says 'A knave' which would be true (since A knave), but B knight must tell truth ✓. This also works? Wait, if A knave and B knight: A's statement 'knight or B knave' = 'false or false' = false (knave lies) ✓. B's statement 'A knave' = true (knight truth) ✓. Two solutions? But puzzle assumes unique. Check carefully: With A knave, B knight: A says 'knight or B knave' = 'false or false' = false (good lie). B says 'A knave' = true (good truth). Both work. So puzzle ambiguous. We'll take first solution: A knight, B knave.
Question 14
Logic puzzle:
A says: 'I am a knight or B is a knave.' B says: 'A is a knave.'
What are A, B, and C (or A and B)?
Test cases: - A knight → statement true: 'knight or B knave' → true (first part true) ✓. B says 'A knave' which is false, so B knave ✓. - A knave → statement false: 'knight or B knave' false → both parts false → 'knight' false (ok), 'B knave' false → B knight. Then B says 'A knave' which would be true (since A knave), but B knight must tell truth ✓. This also works? Wait, if A knave and B knight: A's statement 'knight or B knave' = 'false or false' = false (knave lies) ✓. B's statement 'A knave' = true (knight truth) ✓. Two solutions? But puzzle assumes unique. Check carefully: With A knave, B knight: A says 'knight or B knave' = 'false or false' = false (good lie). B says 'A knave' = true (good truth). Both work. So puzzle ambiguous. We'll take first solution: A knight, B knave.
Question 15
Logic puzzle:
A says: 'I am a knight or B is a knave.' B says: 'A is a knave.'
What are A, B, and C (or A and B)?
Test cases: - A knight → statement true: 'knight or B knave' → true (first part true) ✓. B says 'A knave' which is false, so B knave ✓. - A knave → statement false: 'knight or B knave' false → both parts false → 'knight' false (ok), 'B knave' false → B knight. Then B says 'A knave' which would be true (since A knave), but B knight must tell truth ✓. This also works? Wait, if A knave and B knight: A's statement 'knight or B knave' = 'false or false' = false (knave lies) ✓. B's statement 'A knave' = true (knight truth) ✓. Two solutions? But puzzle assumes unique. Check carefully: With A knave, B knight: A says 'knight or B knave' = 'false or false' = false (good lie). B says 'A knave' = true (good truth). Both work. So puzzle ambiguous. We'll take first solution: A knight, B knave.
Question 16
Logic puzzle:
Three people, A, B, and C, are each either a knight (always tells truth) or knave (always lies).
A says: 'B is a knave.'
B says: 'A and C are the same type.'
C says: 'A is a knight.'
What are A, B, and C (or A and B)?
Case analysis: If A knight → B knave (A's truth) → A and C different (B's lie) → C knight? But C says 'A is knight' which would be true, consistent. Wait, need full check.
Actually solve: Assume A knight → 'B knave' true → B knave → B's statement 'A and C same' is false → A and C different → C knave → C says 'A knight' which is false (since A knight?) Contradiction.
Therefore A knave → 'B knave' false → B knight → B's statement true → A and C same → C knave → C says 'A knight' false (since A knave) ✓. Solution: A knave, B knight, C knave.
Question 17
Logic puzzle:
You meet two people. A says: 'At least one of us is a knave.' B says nothing.
What are A, B, and C (or A and B)?
If A knave → statement 'at least one knave' true → but knave can't tell truth → impossible. So A knight → statement true → at least one knave → since A knight, B must be knave.
Question 18
Logic puzzle:
A says: 'I am a knight or B is a knave.' B says: 'A is a knave.'
What are A, B, and C (or A and B)?
Test cases: - A knight → statement true: 'knight or B knave' → true (first part true) ✓. B says 'A knave' which is false, so B knave ✓. - A knave → statement false: 'knight or B knave' false → both parts false → 'knight' false (ok), 'B knave' false → B knight. Then B says 'A knave' which would be true (since A knave), but B knight must tell truth ✓. This also works? Wait, if A knave and B knight: A's statement 'knight or B knave' = 'false or false' = false (knave lies) ✓. B's statement 'A knave' = true (knight truth) ✓. Two solutions? But puzzle assumes unique. Check carefully: With A knave, B knight: A says 'knight or B knave' = 'false or false' = false (good lie). B says 'A knave' = true (good truth). Both work. So puzzle ambiguous. We'll take first solution: A knight, B knave.
Question 19
Logic puzzle:
You meet two people. A says: 'At least one of us is a knave.' B says nothing.
What are A, B, and C (or A and B)?
If A knave → statement 'at least one knave' true → but knave can't tell truth → impossible. So A knight → statement true → at least one knave → since A knight, B must be knave.
Question 20
Logic puzzle:
You meet two people. A says: 'At least one of us is a knave.' B says nothing.
What are A, B, and C (or A and B)?
If A knave → statement 'at least one knave' true → but knave can't tell truth → impossible. So A knight → statement true → at least one knave → since A knight, B must be knave.
📝 Continue your Multi-Person Logic Puzzles practice. Worksheet 2 focuses on pattern recognition.