Five children A, B, C, D, and E are fighting over who broke the precious vase. Here are their statements:


A: D broke it. 

D: A lied when he said I broke it. 

B: E broke it. 

E: B broke it. 

C: I didn't break it. 


If only one statement is true, who broke the vase?

(Sourced from a textbook. The solutions at the end are not there because I did not purchase it. )

 Apr 9, 2022

B broke the vase.

 Apr 9, 2022

If A's statement is true then it means that C's statement was fake, which means C did break it, but A's statement said that D broke it, and C and D can't both broke the vase, so A's statement is fake;


If B's statement is true then E broke the vase, but C's statment would be fake and make C the one that broke the vase, so B's statement is fake; 


If C's statement is true then D's statement would be fake, so A was telling the truth when he said D broke it, but A's statement is fake, and so D couldn't have broke the vase, so C's statement is fake;


If D's statement is true then A's statement was fake, and that D didn't break the vase. This also means that B and E vouched each other, therefore they didn't break the vase. This statement doesn't cause any error, so C broke the vase. But just to be safe, let's also check E's statement.


E's statement is the same as B's statement, so E's statement is also fake.



Therefore, D's statement is true and C broke the vase.

 Apr 9, 2022

If A or B or E statements are true then C statement should be false

=> A/B/E broke it and C broke it 

Since above conclution contradicts 

A/B/E cannot be true.

If D statement is false, then A or C should be true. If A is true and C is false 

=> D broke it and C broke it (contradicts)

If A is false, the statement by A is false => D did not broke it which contradicts the conclusion that D is false (initial assumption)

Hence only option left is out

D is true => C is false => C broke it

 Apr 10, 2022

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