# Chelsea Player Statement

Eight Chelsea player makes the following statements :

1. Seven of us are lying here.

2. Six of us are lying here.

3. Five of us are lying here.

4. Five of us are lying here.

5. Four of us are lying here.

6. Three of us are lying here.

7. My name is Torres.

8. My name is Lampard.

The last two are Lampard and Torres or maybe Torres and Lampard.

So can you deduce which of the last two is Lampard or Torres?

**Seventh one is Lampard and the eighth is Torres.**

It is given that Persons seven and Eight are Torres and Lampard. So, we have only two possibilities:

P1. Person 7 is Torres and Person 8 is Lampard (i.e., exactly as they stated) OR

P2. Person 7 is Lampard and Person 8 is Torres

If P1 was correct, then both of them told the truth. In that case,

1. The first person’s statement “Seven of us are lying here” must be false (because two persons have told the truth)

2. If the second statement ‘Six of us are lying here’ were true, it implies that two persons told the truth (as already confirmed) and the rest lied. But then, the statement 2 also becomes true, thereby contradicting itself. Hence, the statement can’t be true.

3. Statement **3 could be true** – i.e.,

**five persons lied**and rest

**three told the truth**– the last two that are ‘confirmed’ as true plus the Person 3 himself.

4. Statement 4 is the same as Statement 3. Hence, if statement 3 were true, Statement 4 also must be true (being the same), but then the No. of true statements becomes 4 (two confirmed plus the statements 3 and 4), thereby contradicting the statement 3 (as well as 4). Hence, the statements must be false.

5. If Statement 5 – that four of them were lying, were true, all statements from 5 onwards must be true because we have already confirmed four preceding statements as false. However, Statement 6 can’t be true because it says three of them lied, whereas we have already confirmed four statements as false. This, in turn, implies that statement 5 also is wrong.

Thus, **If P1 were correct**, **all other statements end up contradicting themselves**, leaving **only two statements true**. But it would make the **Statement 2 correct (i.e., six of them lied**, which is already **proven as self-contradictory**. HENCE, **P1 CAN’T BE TRUE**.

Thus, **P2 MUST BE correct**. i.e., **Person 7 is Lampard and Person 8 is Torres . **In this case, both of them lied, thereby making the **Statement 1 true – that seven of them (except Person 1 himself) were lying. Hence the result. **

**7th is Lampard and the 8th is Torres.
**If we consider the statement “X of us are lying here” as “Exactly X of us are lying here” and there are only one player named Lampard and one player named Torres than statement (1) can be true so statements (7),(8) are false and therefore the person saying he is Torres is actually Lampard and vise versa.

Now lets see another approach:

Since statements (3) and (4) are the same than they both can be true or both false. So if they are both true that leaves only one more statements as true and since no other statement of the form: “X of us are lying here” can be true than means than only one of the statements (7), (8) is true and that is not an option so that means that statements (3) and (4) are False.

We know that statements (7), (8) can also both be true or both false.

If they are true than the options are :

>>>> 6 are lying > it contradicts with statement (2)

>>>> 5 are lying > it contradicts with statements (3) and (4)

>>>> 4,3 are lying means there are 2,3 more true statements but statements (1),(2),(5),(6) contradict between themselves so the only solution is that (7) and (8) are false and (1) is true.

### Your Answer

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