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Reworded some things
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Altainia
Altainia
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Let's rewrite the question as follows (I think best in positives...):

! CA: "4 of us are liars"
AB: "6 of us are liars"
DC: "3 of us are liars"
BD: "5 of us are liars"
E: "3 of us are liars"

Now let's figure what we can initially:

A! B can't be truthful; being so would mean he's a liar, which would be contradictory
If BD were truthful, it would mean BD is the only truth-teller (even F would be a liar)
If CA were truthful, it would mean CA is one of two truth-tellers. A, B, D, C and E contradict CA, so if CA were truthful, the mysterious F would have to agree with CA
DC and E are either both truthful or both liars. If they are truthful, it would mean A, B, D and CA are liars so F must be truthful (and agree with DC and E)

From that I conclude multiple possibilities:

! If F says "3 of us are liars" then DC, E and F are truthful only.
If F says "4 of us are liars" then CA and F are truthful only.
If F says anything else, then BD is truthful only.

So...:

! F can say "3 of us are truth-tellers" (Truthies: DC, E, F; Liars: A, B, CD, A)
F can say "2 of us are truth-tellers" (Truthies: CA, F; Liars: A, B, D, C, E)
F can say anything else (Truthies: B;D; Liars: B, A, C, D, E, F)

Let's rewrite the question as follows:

! C: "4 of us are liars"
A: "6 of us are liars"
D: "3 of us are liars"
B: "5 of us are liars"
E: "3 of us are liars"

Now let's figure what we can initially:

A can't be truthful; being so would mean he's a liar, which would be contradictory
If B were truthful, it would mean B is the only truth-teller (even F would be a liar)
If C were truthful, it would mean C is one of two truth-tellers. A, B, D and E contradict C, so if C were truthful, the mysterious F would have to agree with C
D and E are either both truthful or both liars. If they are truthful, it would mean A, B and C are liars so F must be truthful (and agree with D and E)

From that I conclude multiple possibilities:

If F says "3 of us are liars" then D, E and F are truthful only.
If F says "4 of us are liars" then C and F are truthful only.
If F says anything else, then B is truthful only.

So...:

F can say "3 of us are truth-tellers" (Truthies: D, E, F; Liars: A, B, C)
F can say "2 of us are truth-tellers" (Truthies: C, F; Liars: A, B, D, E)
F can say anything else (Truthies: B; Liars: A, C, D, E, F)

Let's rewrite the question as follows (I think best in positives...):

! A: "4 of us are liars"
B: "6 of us are liars"
C: "3 of us are liars"
D: "5 of us are liars"
E: "3 of us are liars"

Now let's figure what we can initially:

! B can't be truthful; being so would mean he's a liar, which would be contradictory
If D were truthful, it would mean D is the only truth-teller (even F would be a liar)
If A were truthful, it would mean A is one of two truth-tellers. B, D, C and E contradict A, so if A were truthful, the mysterious F would have to agree with A
C and E are either both truthful or both liars. If they are truthful, it would mean B, D and A are liars so F must be truthful (and agree with C and E)

From that I conclude multiple possibilities:

! If F says "3 of us are liars" then C, E and F are truthful only.
If F says "4 of us are liars" then A and F are truthful only.
If F says anything else, then D is truthful only.

So...:

! F can say "3 of us are truth-tellers" (Truthies: C, E, F; Liars: B, D, A)
F can say "2 of us are truth-tellers" (Truthies: A, F; Liars: B, D, C, E)
F can say anything else (Truthies: D; Liars: B, A, C, E, F)

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Altainia
Altainia
  • 301
  • 1
  • 5

Let's rewrite the question as follows:

! C: "4 of us are liars"
A: "6 of us are liars"
D: "3 of us are liars"
B: "5 of us are liars"
E: "3 of us are liars"

Now let's figure what we can initially:

A can't be truthful; being so would mean he's a liar, which would be contradictory
If B were truthful, it would mean B is the only truth-teller (even F would be a liar)
If C were truthful, it would mean C is one of two truth-tellers. A, B, D and E contradict C, so if C were truthful, the mysterious F would have to agree with C
D and E are either both truthful or both liars. If they are truthful, it would mean A, B and C are liars so F must be truthful (and agree with D and E)

From that I conclude multiple possibilities:

If F says "3 of us are liars" then D, E and F are truthful only.
If F says "4 of us are liars" then C and F are truthful only.
If F says anything else, then B is truthful only.

So...:

F can say "3 of us are truth-tellers" (Truthies: D, E, F; Liars: A, B, C)
F can say "2 of us are truth-tellers" (Truthies: C, F; Liars: A, B, D, E)
F can say anything else (Truthies: B; Liars: A, C, D, E, F)