Question

36 Fourfriends have been identified as suspects for an unauthorized access into a computer system. 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.”

a) If the authorities also know that exactly one of the four suspects is telling the truth, which did it? Explain your reasoning.

b) If the authorities also know that exactly one is lying, who did it? Explain your reasoning.

Short answer

Part (a) John had unauthorized access.

Part (b) it was Carlos who had unauthorized access.

Step-by-step solution

Tips

(a)

To make such statements precise, they can be translated into the language of logic.

Find the person is lying or speaking the truth

First of all we notice that Carlos and Diana cannot be both lying.

If Carlos is lying, then Diana would be telling the truth and if Carlos is telling the truth the Diana would be lying.

So it is either Carlos or Diana telling the truth.

John is lying and tells that I didn't do that.

Therefore, John had unauthorized access.

First solve: All we notice that Carlos and Diana cannot be both laying.

Then solve: John had unauthorized access finally solve all given conditions

Tips

(b)

Puzzles that can be solved using logical reasoning are known as logic puzzles. Solving logic puzzles is an excellent way to practice working with the rules of logic.

Find the person is lying or speaking the truth

Carlos and Diana both cannot be telling the truth, so the liar is either Carlos or Diana.

This means that Alice is telling the truth.

Alice said: “Carlos did it”.

Therefore, it was Carlos who had unauthorized access.