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So, I think I got it as well. Only one door is safe, so that means only one guard is telling the truth.

Guard 1:

He could be telling the truth (since it doesn't say he ONLY tells the truth if all others are telling the truth), but it isn't certain because the other four are definitely not all telling the truth.

Guard 2:

There are 2 possibilities: If Guard 1 has lied, he is a liar according to his statement. If Guard 1 told the truth, then since there is only one speaking the truth, Guard 2 is still a liar. Thus, we can conclude that Guard 2 is a liar.

Guard 3:

He's a liar, but that is not relevant for searching the truth-teller.

Guard 4:

4 lairs, 1 truth-teller. That means, he's a liar according to his own statement.

Guard 5:

We have deduced that #2 and #4 are liars, so he's telling the truth and therefore his door is safe. We can also conclude that the unknown, #1, is a liar because the truth of #5 is 100% certain and therefore eliminates #1.

To conclude:

Guard 5's door is safe.

After looking at the other answers, I'm glad I got here after the edits were made, it was much clearer.

So, I think I got it as well. Only one door is safe, so that means only one guard is telling the truth.

Guard 1:

He could be telling the truth (since it doesn't say he ONLY tells the truth if all others are telling the truth), but it isn't certain because the other four are definitely not all telling the truth.

Guard 2:

There are 2 possibilities: If Guard 1 has lied, he is a liar according to his statement. If Guard 1 told the truth, then since there is only one speaking the truth, Guard 2 is still a liar. Thus, we can conclude that Guard 2 is a liar.

Guard 3:

He's a liar, but that is not relevant for searching the truth-teller.

Guard 4:

4 lairs, 1 truth-teller. That means, he's a liar according to his own statement.

Guard 5:

We have deduced that #2 and #4 are liars, so he's telling the truth and therefore his door is safe. We can also conclude that the unknown, #1, is a liar because the truth of #5 is 100% certain and therefore eliminates #1.

To conclude:

Guard 5's door is safe.

So, I think I got it as well. Only one door is safe, so that means only one guard is telling the truth.

Guard 1:

He could be telling the truth (since it doesn't say he ONLY tells the truth if all others are telling the truth), but it isn't certain because the other four are definitely not all telling the truth.

Guard 2:

There are 2 possibilities: If Guard 1 has lied, he is a liar according to his statement. If Guard 1 told the truth, then since there is only one speaking the truth, Guard 2 is still a liar. Thus, we can conclude that Guard 2 is a liar.

Guard 3:

He's a liar, but that is not relevant for searching the truth-teller.

Guard 4:

4 lairs, 1 truth-teller. That means, he's a liar according to his own statement.

Guard 5:

We have deduced that #2 and #4 are liars, so he's telling the truth and therefore his door is safe. We can also conclude that the unknown, #1, is a liar because the truth of #5 is 100% certain and therefore eliminates #1.

To conclude:

Guard 5's door is safe.

After looking at the other answers, I'm glad I got here after the edits were made, it was much clearer.

Source Link

So, I think I got it as well. Only one door is safe, so that means only one guard is telling the truth.

Guard 1:

He could be telling the truth (since it doesn't say he ONLY tells the truth if all others are telling the truth), but it isn't certain because the other four are definitely not all telling the truth.

Guard 2:

There are 2 possibilities: If Guard 1 has lied, he is a liar according to his statement. If Guard 1 told the truth, then since there is only one speaking the truth, Guard 2 is still a liar. Thus, we can conclude that Guard 2 is a liar.

Guard 3:

He's a liar, but that is not relevant for searching the truth-teller.

Guard 4:

4 lairs, 1 truth-teller. That means, he's a liar according to his own statement.

Guard 5:

We have deduced that #2 and #4 are liars, so he's telling the truth and therefore his door is safe. We can also conclude that the unknown, #1, is a liar because the truth of #5 is 100% certain and therefore eliminates #1.

To conclude:

Guard 5's door is safe.