Difficulty ★★☆about 5 minLogic PuzzleTrue or false statementsCase analysis
There is exactly one thief, and only the thief lies. Check each case against the three statements to name the thief.
Case Record
Goods were stolen from a warehouse. The suspects are Araki, Inoue and Uno. Exactly one of them is the thief, and it is known that only the thief lies; the other two tell the truth.
Their statements are as follows.
Araki: "Inoue stole it."
Inoue: "I did not steal it."
Uno: "Araki is lying."
Your question
Who is the thief?
Case Files
Evidence
E-1Araki’s statement"Inoue stole it."
E-2Inoue’s statement"I did not steal it."
E-3Uno’s statement"Araki is lying."
Diagram
Diagram
Timeline
The theft from the warehouse comes to light.
The three give their statements.
Only the thief lies.
Hints
If you get stuck, open the hints one at a time, in order.
Open hint 1
Pick one person as the thief and check whether all three statements satisfy the condition.
Open hint 2
If you end up with two liars, that assumption is wrong.
Assume each person is the thief in turn and check whether "only the thief lies, the others tell the truth" holds.
If Araki is the thief, "Inoue stole it" is a lie. Inoue’s "I did not steal it" is true. Uno’s "Araki is lying" is also true. The condition is satisfied.
If Inoue is the thief, Araki’s "Inoue stole it" is true and Inoue’s "I did not steal it" is a lie. So far so good, but then Uno’s "Araki is lying" is false, which makes Uno (not the thief) a liar. Contradiction.
If Uno is the thief, Araki’s "Inoue stole it" is false, so Araki would be a liar too.
Only the case where Araki is the thief holds without contradiction.
Diagram of the solution
Key Points
Assume a culprit and check everyone’s statement
See whether the liar count is exactly "the culprit alone"
When only one assumption holds, that is the answer
Why people get fooled
If you believe the first statement, "Inoue stole it," Inoue starts to look guilty. Without the habit of testing each assumption, you jump to conclusions.
Similar tricks
The liar puzzle solved by case analysis
The type where you eliminate cases by contradiction
