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### Logic Statements Puzzle

Logic Statements Puzzle - 15 April

Eight Chelsea player makes 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 last two is Lampard or Torres ?

1. 7 lampard
8 torres

2. 7 lampard
8 torres

3. let the statements 7,8 be true:then
1.The statement 2 cannot be true since the remaining 6 statements(i.e leaving 7,8) should be lies..which is not possible
2.statement 6 is also lie bcoz if that is true there will be atleast 1 statement that contradicts this statement(as there are 4 possibilities leaving statements 2,6,7,8)
3.statements 3,4 are also lies bcoz if it is true then statements 3,4 will be true and the total no.of lies is only 4(1,2,5,6)
4.statement 5 is also lies bcoz if 4 are lies then statement 1 should also be a lie which contradicts this statement
5.so there are only 5 lies in total so..statement 1 is also a lie
6.So,now we got all lies...so statements 7,8 are true is a contradiction..so statements 7,8 are false..so 7 is Lampard and 8 is Torres :)

This can be proven in the other way also taking statements 7,8 are lies
If 7,8 are lies then
1.statement 6 is also alie bcoz there will be atleast 4 statements which will contradict this statement(by removing 7,8,3 and other 1 lie)
2.now we have 3 lies..so statement 5 is also a lie bcoz there will be atleast 2 lie which contradicts this statement(removing 7,8,6,(3,4) or 2 or 1)
3.statements 3,4 are also lies bcoz now we have 4 lies,if there are 5 lies then one of the 1,2 should be lie and the other is true which is not possible
4.statement 2 is also lies bcoz now we have 6 lies..if statement 2 is true then statement 1 will be lies and we'll have 7 lies so the statement 2 is lies
5.now that we have 7 lies..statement 1 is true
So,there is a true statement satisfying all the possibilities when statements 7,8 are lies..so 7 is Lampard and 8 is Torres..cheers!! :D :D

4. Logic:
7 Lampard
8 Torres

Only statement 1 is true (7 are lies)

5. Philosophy:
7 Torres
8 Lampard

Only statement 1 is false (7 are true)