Bite-sized brain teaser to solve in a minute or less.
The Suspect Statements
Four people are suspects in a minor theft at a community event. They each make one statement:
Statement 1 - Alex: “I didn’t do it.”
Statement 2 - Blake: “I was with Chris when it happened.”
Statement 3 - Chris: “I was completely alone at the time.”
Statement 4 - Dana: “Blake is lying.”
It is known that only one of these statements is true. Who is the culprit?
Solution
We know exactly one of these statements is true.
Statement 1: Assume Statement 1 (Alex’s statement) is the only true statement.
Then Alex did not do it.
But then Statement 4 (“Blake is lying”) must be false, meaning Blake is telling the truth (Statement 2 true).
Also, Statement 3 (“I was alone”) is false, so Chris was not alone.
However, if Statement 2 is true (Blake was with Chris), then Chris’s statement Statement 3 would be false (which is allowed) but then we’d have Statement 1 and Statement 2 both true.
This violates the rule of only one true statement.
Statement 2: Assume Statement 2 (Blake’s statement) is the only true statement.
Then Blake was with Chris.
Then Statement 1 is false, so Alex’s statement “I didn’t do it” is false; hence, Alex did it.
Statement 3 is also false, meaning Chris was not alone—which is consistent with being with Blake.
Statement 4 is false as well, so Dana’s claim “Blake is lying” is false; hence, Blake is telling the truth (which agrees with our assumption).
Only Statement 2 is true and all conditions are consistent.
Statement 3: Assume Statement 3 (Chris’s statement) is the only true statement.
Then Chris was alone.
Statement 1 is false, so Alex did it.
Statement 2 is false, so Blake was not with Chris.
Statement 4 is false, so Dana’s statement “Blake is lying” would be false, meaning Blake would be telling the truth. But that contradicts Statement 2 being false.
This case fails.
Statement 4: Assume Statement 4 (Dana’s statement) is the only true statement.
Then Blake is lying, so Statement 2 is false.
Statement 1 is false, so Alex did it.
Statement 3 is false, so Chris was not alone.
But if Chris was not alone, then he must have been with someone. The only remaining possibility for a pairing would be Blake. However, that would make Statement 2₂ (“I was with Chris”) true, contradicting our assumption.
This case fails.
Conclusion:
Only Statement 2 yields a consistent scenario. In this case, only Blake’s statement is true, and Alex’s statement being false means Alex committed the theft.
