Andrew and Bob

It's impossible for only one of them to be lying, because that would entail that they both have the same name, which we know isn't the case.

Since we know that at least one of them lied, we deduce that both must be lying, which means we have to swap the names we are given: Bob wears a blue shirt and Andrew wears a red shirt.

The latter statement is the answer to the problem. That is, Bob is the one wearing the red shirt.

First, we could see that they must be both lying or both telling the truth. But we are told that there is at least one person lying. Hence, they are both lying and Andrew is wearing a red shirt.

Let's consider cases based on who lied and who told the truth. We will show that the only possible case is for both to have lied.

Case 1: Both told the truth
Since we are told that at least one of them lied, it cannot be the case that both of them told the truth.

Case 2: Blue shirt lied, red shirt told the truth
If only the person in the blue shirt lied, then he would be Bob, and the person in the red shirt would be Bob. Since neither of them are Andrew, this is not possible.

Case 3: Red shirt lied, blue shirt told the truth
Similarly, if only the person in the red shirt lied, then he would be Andrew, and the person in the blue shirt would be Andrew. Since neither of them are Bob, this is not possible.

Case 4: Both lied Since the other 3 cases have been eliminated, this leaves us with the case that both of them are lying. Hence the person in the blue shirt is Bob and the person in the red shirt is Andrew.

The keyword is 'AT LEAST ONE of them lied'

Using pseudo-boolean logic operators:

If (blue is Andrew && blue said Andrew) = true,

• Then (red is Bob && red said Bob) = true; ( If blue is Andrew, then red has to be Bob ) (If one of them is telling the truth, they both are telling the truth)

However, the rules state that they cannot all be telling the truth. (There must be at least one liar).

Therefore try:

If (blue is Bob && blue said Andrew) = liar,

• Then (red is Andrew && red said Bob) = liar. Rule stipulates that they can both be telling the truth, therefore SUCCESS.

Final evaluation

If they are both liars and there are only two names , then the name of the person in the blue or red shirt must be the opposite of their assertion.

Also see: If (blue is Andrew && blue said Andrew) = true; Then (red is Andrew && said Bob). -> i.e. Cannot both be the same person.

There are also other lateral solutions to this problem that exploit the ambiguity of the rules.

The statement is saying that if we know that at "least" one of them lied, what color shirt is Andrew wearing. "At least", so, one of them was lying or MAY BE both of them were lying.

Now, look at their names. If one of them is lying, then problably there will be two guys with the same name... it will be like this:

If the guy in blue shirt was lying: blue shirt: "I am Bob" Then, the guy in red shirt was honest: Red shirt: "I am Bob"

If the guy in red shirt was lying: red shirt: "I am Andrew" Then, the guy in blue shirt was honest: blue shirt: "I am Andrew"

We have 2 guys with different name here, so PROBLABLY, both of them are lying? Why? Look at the statement "at least one of them lied", so it is problably that one or both of them lied.

Okay, now the answer is red. Because both of them lied, so the Andrew in that picture is actually Bob, and the Bob in that picture is actually Andrew. And it will be Andrew is the guy with red shirt, and Bob is the guy with blue shirt.

One of them lied. It simply means shirt's color he told was also a lie. Thus situation reverses so it tends bob wore blue and Andrew Red.

I think there are only 2 person at least one of them lied that itself mean bothe lied in this scenario. So interchange what they said. Andrew will be bearing Red.

If one of them are lying, the other one should be lying too. Therefore, we know that if both are lying, Andrew is lying about being the blue shirt. So, Andrew is the one in the red shirt.

You as what ANdrew is wearing, if andrew is lying then his shirt is red, and if Bob is lying then his shirt is blue. In both circumstances Andrew has the red shirt.

If only one of them lied then there is a mismatch. So, both of them lied.

they both have to be lying because it can not be only 1 person is lying

Since both stated a different name and at least one must be lying, then both had to be lying.

Problem states that alteast one is lyiing case 1: Atleast one is lying. This is not possible that if only blue shirt lies about being Andrew then he must be Bob, which implies that Red shirt is lying which contrary to our assumption that only one is lying. Hence this case is not possible hence both Red and blue shirts are lying

case 2: Both are lying. In this case we can just switch the names that the Red Shirt guys says.

Lets consider all the possibilities:

$(Blue, Red)$

1 $(T, L)$

2 $(L, T)$

3 $(L, L)$

It's easy to see that case 1 will lead to a contradiction. If Blue is truthful he is Andrew, however this cannot be as by lying Red is also implying that he is Andrew and since there can't be two Andrews, 1 is impossible.

Similarly, we can use the same logical statements to show that 2 is impossible.

This leaves us with case 3 which implies that Blue is Bob and that Red is Andrew.

We know that at least one of them has to be lying, however, they both could be. Since there is only two of them, and they both say a different name, we deduce that both of them have to be lying. This means they must have the opposite name of the one they say, ergo andrew is wearing the red shirt!

Red shirtt. cause both are lying

Obviously, there are only two colors, and only two boys. Even if one is lying, the colors must flip. The case is, most probably, the same If both of then lie together...

Assume both of them are lying as it says at least one of them is

The statement says that atleast one lies,so there cannot be case of both telling the truth . So the andrew is wearing red.

Didn't say they lied about their name

given facts : we have two poeple bob and andrew we just don't know who is bob and who is andrew ... the guy in the red shirt said that he was bob and the guy in the blue shirt said that he was andrew ... at least on of them is lying ... conc : since only two people are talking then if one of them is lying certainly the other one is lying too ... then the guy wearing the red shirt is andrew and the guy wearing the blue shirt is bob