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# Who am I?

## Question

We are taking one statement from each of eight people. The last two are Bill and Susan, or maybe Susan and Bill. Anyway, one of those two is Susan, the other is Bill. See if you can deduce which is Bill and which is Susan:

1. Exactly seven of us are lying.
2. Exactly six of us are lying.
3. Exactly five of us are lying.
4. Yes, exactly five of us are lying.
5. Exactly four of us are lying.
6. Exactly three of us are lying.
7. My name is Susan.
8. My name is Bill.

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The Only non contradictory case is :

1 is true - in that case 7 = Susan and 8 = Bill

Made an error both 7 and 8 are lying (only 1 is speaking truth. So 7 = Bill and 8 = Susan

Edited by bonanova
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#1 spoke the truth and the rest lied

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The Only non contradictory case is :

1 is true - in that case 7 = Susan and 8 = Bill
Edited by nakulendu
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It is not possible to deduce about Bill and Susan the way problem is stated.

Some extra condition, for example about number of true statements, is required.

Edited by witzar
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From the OP it is clear that statements [7 & 8] are both either true or lie.

CASE - 1
Assuming both as true, we get the following results:
Statement [1] is lie, as seven of them couldn't be lying.
[2] is lie, as six of them couldn't be lying if [2] was true.
[3] & [4] are both either lie are both true. So [3] & [4] both are lies, as five of them couldn't be lying if [3] & [4] both were true.
Either one of [5] & [6] could be true, so [5] couldn't be true, if [6] was a lie. Also [6] couldn't be true if [5] was a lie. Therefore both are lie.
Conclusion of above: If [7] & [8] were true, thenl other six would be lying, which would make the statement [2] - true, So case - 1 is not possible.
CASE - 2:
[7] & [8] both are lying. then all of the statements become lie except [1]. Therefore Case - 2 is correct. Both [7] & [8] are lying hence [7] is Bill and [8] is Susan.

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all lying - 7-bill 8-susan

1 true rest lying 7- bill, 8-susan

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all lying - 7-bill 8-susan

1 true rest lying 7- bill, 8-susan

All can't lie, because Statement 1 becomes true as soon as seven are considered lie. It is really amazing isn't it...?

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all lying - 7-bill 8-susan

1 true rest lying 7- bill, 8-susan

All can't lie, because Statement 1 becomes true as soon as seven are considered lie. It is really amazing isn't it...?

But there are 8 people. If all of them lie, then statement 1 is false.

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all lying - 7-bill 8-susan

1 true rest lying 7- bill, 8-susan

All can't lie, because Statement 1 becomes true as soon as seven are considered lie. It is really amazing isn't it...?

But there are 8 people. If all of them lie, then statement 1 is false.

Please think again. There are 8 statements given in OP. If first statement is also considered to be a lie then there will be 8 false statements, but we can not make forced opinion. We have to go by statements available with us.

More clearly to say is that even if first person wanted to lie, he could not lie by giving this statement.

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Very nice argument, sadly Nakluendo beat you to it.

From the OP it is clear that statements [7 & 8] are both either true or lie.

CASE - 1

Assuming both as true, we get the following results:

Statement [1] is lie, as seven of them couldn't be lying.

[2] is lie, as six of them couldn't be lying if [2] was true.

[3] & [4] are both either lie are both true. So [3] & [4] both are lies, as five of them couldn't be lying if [3] & [4] both were true.

Either one of [5] & [6] could be true, so [5] couldn't be true, if [6] was a lie. Also [6] couldn't be true if [5] was a lie. Therefore both are lie.

Conclusion of above: If [7] & [8] were true, thenl other six would be lying, which would make the statement [2] - true, So case - 1 is not possible.

CASE - 2:

[7] & [8] both are lying. then all of the statements become lie except [1]. Therefore Case - 2 is correct. Both [7] & [8] are lying hence [7] is Bill and [8] is Susan.

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