Three of these statements are false, so who did it?
- Mr Red: “Mr Blue did it.”
- Mr Blue: “Mr Red did it.”
- Mr Green: “Mr Blue’s telling the truth.”
- Mr Yellow: “Mr Green’s not lying.”
See Solution
Answer: Mr Blue did it.
How?
Lets consider all the cases when one of Mr did it, and then we will see how many statements are true and how many of them are false, we should get 3 false and 1 true statements.
Case 1: Mr Blue did it, then
statement 1 => true
statement 2 => false(as red did not do it)
statement 3 => false (as Mr Blue is lying)
statement 4 => false (as Mr Green is lying)
Gotcha, in the very first attempt we found one of the answer, Mr Blue did it, now we will see if others did it or not 🙂
Case 2: Mr Red did it, then
statement 1 => false(as Mr Blue did not do it)
statement 2 => true
statement 3 => true(as Mr Blue is not lying)
As two statements are coming out as true, we can say Mr Red did not do it 🙂
Case 3: Mr Green did it, then
statement 1 => false(as Mr Blue did not do it)
statement 2 => false(as Mr Red did not do it)
statement 3 => false (as Mr Blue is lying)
statement 4 => false (as Mr Green is lying)
In this case all four statements are false, so we can say Mr Green did not do it.
Case 4: Mr Yellow did it, then
statement 1 => false(as Mr Blue did not do it)
statement 2 => false(as Mr Red did not do it)
statement 3 => false (as Mr Blue is lying)
statement 4 => false (as Mr Green is lying)
In this case all four statements are false, so we can say Mr Yellow did not do it.
A simpler solution may be….
Assume Mr. Yellow is telling truth. Then, Mr. Green is also telling truth. But, it is sure that only one statement is true. It means, Mr. Yellow is telling false. It makes Mr. Green is also telling false. From Mr. Green statement, it can be deduced that Mr. Blue is also telling false. Thus, only Mr. Red is telling the truth, which means Mr. Blue did it.