Unauthorized access

Level 2

Four friends have been identified as suspects for an unauthorized access into a computer system, of whom exactly one has committed the crime. They have made statements to the investigating authorities.

Alice said, “Carlos did it.”

John said, “I did not do it.”

Carlos said, “Diana did it.”

Diana said, “Carlos lied when he said that I did it.”

If the authorities also know that exactly one of the four suspects is telling the truth, then who did it?

1) Alice

2) Carlos

3) Diana

4) John

4 1 2 3

Prerona Chatterjee by Prerona Chatterjee , 28, India

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3 solutions

Saya Suka
Feb 11, 2021

Carlos & Diana were being contradictory, so either one of them must have told the truth and nobody else would or could by what the authorities found out. Alice and John were definitely lying, so with John's self-claiming innocence, it's obvious he's our guilty criminal.

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The Person who knows he is criminal can't blame other confidently.

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You need to reason backwards. Essentially, since we know one person is speaking the truth, we can thus infer that three people are lying. Analyse, one by one, what would be the outcomes if one person says the truth and three lie.

Let's start with Alice as the truth-speaker. That means, the others are lying. Effectively, it means Alice actually means Carlos did it. However, if John's statement is false, it means he is also guilty, which is not possible as we know only one person is guilty.

Moving on to John as being the true one, it means he didn't do it, but also that Carlos didn't do it, and neither did Diana. This also means Carlos was truthful, which means Diana did it, which is counterintuitive to our previous deduction.

Now, if Carlos is true, it means Diana did it, but Carlos didn't. This also means Diana did it, but thus implies Diana is saying the truth, as her statement now agrees with Carlos'.

Finally, assuming Diana is true, it means neither she, nor Carlos did it. IT IMPLIES JOHN IS LYING, AND THUS, HE IS OUR PERPETRATOR.

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