I Did Not Do It

Logic Level 2

Alex, Benny and Charlie were suspected of hacking a bank. When questioned, they said:

Alex: I did not do it.
Benny: Charlie did it.
Charlie: Alex did it.

If only one of them is telling the truth, and one of them hacked the bank, who is guaranteed to be innocent ?

Alex Benny Charlie Not enough information

View wiki
Chung Kevin by Chung Kevin , 46, Australia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Chung Kevin
Jul 1, 2016

Let's consider cases based on who told the truth

Case 1: Alex told the truth
Alex's statement: Alex did not do it
Benny's statement: Charlie did not do it
Charlie's statement: Alex did not do it
So we conclude that Benny is guilty.

Case 2: Benny told the truth
Alex's statement: Alex did it
Benny's statement: Charlie did it Charlie's statement: Alex did not do it
This scenario is not possible.

Case 3: Charlie told the truth Alex's statement: Alex did it
Benny's statement: Charlie did not do it Charlie's statement: Alex did it
So we conclude that Alex is guilty.

Since Case 1 and Case 3 are possible, we conclude that the only person who is innocent is Charlie. It's possible for Alex or Benny to be guilty.

8 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

There isn't a need to check all 3 cases.

A simpler way to solve this is to notice that Alex and Charlie made contradictory claims, that is, one of them is lying while the other is telling the truth. Since we have established that exactly one of Alex and Charlie is telling the truth, Benny must have told a lie. Hence, Benny's claim is false, which implies Charlie did not do it (i.e. is innocent) .

(IF )Alex is true-teller this lead us to a conclusion that both Benny and Charlie are liar-tellers and thus,Alex didnot hack the bank and Beny's statement is false so charlie didnot hack ...the same thing with Charlie's statement so alex didnot hack so this leads to a confusion between the three men

then i can conclude that Alex is false so he stole the bank and Benny is false too so Charlie didnot steal the bank but for charlie's statment must be true so this implies that (alex) stole the bank

Mina Aziz - 4 years, 11 months ago
Kalpok Guha
Jun 27, 2016

If Benny is telling truth.Then Alex and Charlie must lie.

Alex said 'I did not do it'.He was lying ,which implies that he did it.But we have assumed that Benny was telling truth,Benny said 'Charlie did it',which implies Charlie did it.Which leads to a contradiction.

Hence we can say Benny was lying.Which implies Charlie did not do it.Thus we can say Charlie is innocent.

3 Helpful 0 Interesting 0 Brilliant 1 Confused

We can only conclude that Charlie is innocent. We do not know who is guilty! Depending on whether Alex or Charlie told the truth, the guilty party respectively is Benny or Alex.

Chung Kevin - 4 years, 11 months ago

I dont agree with you...... I think that if we assume to charlie speaking the truth then alex is false and he has done the crime and also benny is not speakin the truth that is charlie is speaking the truth and benny might be innocwnt whereas alex is surely the criminal

Atharva Bagul - 4 years, 11 months ago

Log in to reply

In this case you have assumed that Charlie is speaking truth,what will happen if Charlie is lying ?

Kalpok Guha - 4 years, 11 months ago

Log in to reply

Then what if benny is lying??

Atharva Bagul - 4 years, 11 months ago

Log in to reply

@Atharva Bagul – I have proved that Benny cannot tell truth.He is lying.And you are asking 'what if benny is lying',please read the solution and then ask questions.

Kalpok Guha - 4 years, 11 months ago

If Charlie is speaking the truth, then Alex did it and so Charlie is innocent, which doesn't contradict the answer. Of course, Benny is also innocent.

The question asks who do we know must be innocent. You have to consider all the possible cases given the information. If Alex was the one that told the truth, then Benny is guilty (so Benny is not the answer). However, in all the possible scenarios, Charlie is always innocent.

Chung Kevin - 4 years, 11 months ago

Log in to reply

You don't have to consider all possible cases to know which should be the innocent person or you don't have to at least from the data of the problem anyway but you , at most , should consider them to check their consistency regarding the fact that Charlie is innocent and indeed there 2 possible solutions.

You can just observe that A's and C's statements are contradictory and therefore because there is only one true statement that statement must be one of A or C meaning that B's statement is necessarily false from which because that statement is a declarative one "Charlie is guilty" you conclude Charlie is innocent.

A A - 4 years, 11 months ago

Log in to reply

@A A – I am explaining why there is no other person that can be declared innocent. If you work with the assumption that the question is correctly phrased and that a unique answer exists, then your approach suffices. However, I think the solution should be self-contained, and apply even if we were given a different set of options (e.g. if the options included "Benny and Charlie").

Chung Kevin - 4 years, 11 months ago

Log in to reply

@Chung Kevin – Yes , you are right. The reasoning I provided would be incomplete because it doesn't speak about the innocence of the other persons , this being the thing asked by the problem , and it can be , from a rigorous point of view , being based on the assumption of the consistency of the problem's statements flawed anyway.

Yet one small remark. I think a better word for the solution being as you said self-contained would be rather auto-sustainable as it is solid independently.

A A - 4 years, 11 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...