We have five statements to process:

1. "Two of us are truth tellers".
2. "None of us are truth tellers".
3. "Three of us are truth tellers".
4. "Only one of us is a truth teller".
5. "Three of us are truth tellers".

These five statements are all mutually contradictory except 3) and 5). So out of the first five speakers, either none, one, or two are telling the truth.

• If none of the first five speakers are telling the truth, then both speaker 2) and speaker 4) are lying, so the number of truth-tellers among all six must be at least two. Contradiction.

• If two of the first five speakers are telling the truth, then it must be speaker 3) and speaker 5), so speaker 6) must be the third truth-teller, so speaker 6) must also say "Three of us are truth tellers". However, if speaker 6) does say this, then as far as the foreigner knows, it might be speaker 4) and nobody else telling the truth. This contradicts the assumption that speaker 6)'s statement is enough for the foreigner to know how many truth-tellers there are in total.

So exactly one of the first five speakers is telling the truth. That means speakers 2), 3), and 5) are lying, so the truth-teller among them must be either 1) or 4).

• If it's 1), then speaker 6) must be the second truth-teller, so speaker 6) must also say "Two of us are truth tellers". However, as before, if speaker 6) does say this, then as far as the foreigner knows, it might be speaker 4) and nobody else telling the truth. Contradiction.

So speaker 4) is telling the truth, which means

there is exactly one truth-teller in total.

Now what must speaker 6)'s response have been? It must be a lie, so it can't be "Only one of us is a truth-teller". It also can't be "Two of us are truth-tellers" (since then as far as the foreigner knows, it could have been speakers 1) and 6) telling the truth) or "Three of us are truth-tellers" (since then as far as the foreigner knows, it could have been speakers 3), 5) and 6) telling the truth). Any of the other options seems to be possible. So speaker 6) could have said

"None of us are truth-tellers" or "Four of us are truth-tellers" or "Five of us are truth-tellers" or "All of us are truth-tellers".

We have five statements to process:

1. "Two of us are truth tellers".
2. "None of us are truth tellers".
3. "Three of us are truth tellers".
4. "Only one of us is a truth teller".
5. "Three of us are truth tellers".

These five statements are all mutually contradictory except 3) and 5). So out of the first five speakers, either none, one, or two are telling the truth.

• If none of the first five speakers are telling the truth, then in particular both speaker 2) and speaker 4) are lying, so the number of truth-tellers among all six cannot be zero or one. Contradiction.

• If two of the first five speakers are telling the truth, then it must be speaker 3) and speaker 5), so speaker 6) must be the third truth-teller, so speaker 6) must also say "Three of us are truth tellers". However, if speaker 6) does say this, then as far as the foreigner knows, it might be speaker 4) and nobody else telling the truth. This contradicts the assumption that speaker 6)'s statement is enough for the foreigner to know how many truth-tellers there are in total.

So exactly one of the first five speakers is telling the truth. That means speakers 2), 3), and 5) are lying, so the truth-teller among them must be either 1) or 4).

• If it's 1), then speaker 6) must be the second truth-teller, so speaker 6) must also say "Two of us are truth tellers". However, as before, if speaker 6) does say this, then as far as the foreigner knows, it might be speaker 4) and nobody else telling the truth. Contradiction.

So speaker 4) is telling the truth, which means

there is exactly one truth-teller in total.

Now what must speaker 6)'s response have been? It must be a lie, so it can't be "Only one of us is a truth-teller". It also can't be "Two of us are truth-tellers" (since then as far as the foreigner knows, it could have been speakers 1) and 6) telling the truth) or "Three of us are truth-tellers" (since then as far as the foreigner knows, it could have been speakers 3), 5) and 6) telling the truth). Any of the other options seems to be possible. So speaker 6) could have said

"None of us are truth-tellers" or "Four of us are truth-tellers" or "Five of us are truth-tellers" or "All of us are truth-tellers".

We have five statements to process:

1. "Two of us are truth tellers"
2. "None of us is a truth teller"
3. "Three of us is a truth teller"
4. "Only one of us is a truth teller"
5. "Three of us is a truth teller".

These five statements are all mutually contradictory except 3) and 5). So out of the first five speakers, either none, one, or two are telling the truth.

• If none of them (the first five speakers) are telling the truth, then both speaker 2) and speaker 4) are lying, so the number of truth-tellers among all six must be at least two. Contradiction.

• If two of them are telling the truth, then it must be speaker 3) and speaker 5), so speaker 6) must also be telling the truth, and speaker 6) must say "Three of us are truth tellers". However, if speaker 6) does say this, then it would also be possible for speaker 4) and nobody else to be telling the truth. This contradicts the assumption that speaker 6)'s statement is enough for the foreigner to tell how many truth-tellers there are in total.

So exactly one of the first five speakers is telling the truth. That means speakers 2), 3), and 5) are lying, so the truth-teller must be either 1) or 4).

• If it's 1), then speaker 6) must be the second truth-teller, so speaker 6) must also say "Two of us are truth tellers". However, as before, if speaker 6) does say this, it would also be possible for speaker 4) and nobody else to be telling the truth, contradiction.

So speaker 4) is telling the truth, which means

there is exactly one truth-teller in total.

Now what must speaker 6)'s response have been? It must be a lie, so it can't be "Only one of us is a truth-teller". It also can't be "Two of us are truth-tellers" (since then it could have been speakers 1) and 6) who were telling the truth) or "Three of us are truth-tellers" (since then it could have been speakers 3), 5) and 6) who were telling the truth). Any of the other options seems to be possible. So speaker 6) could have said

"None of us are truth-tellers" or "Four of us are truth-tellers" or "Five of us are truth-tellers" or "All of us are truth-tellers".

We have five statements to process:

1. "Two of us are truth tellers".
2. "None of us are truth tellers".
3. "Three of us are truth tellers".
4. "Only one of us is a truth teller".
5. "Three of us are truth tellers".

These five statements are all mutually contradictory except 3) and 5). So out of the first five speakers, either none, one, or two are telling the truth.

• If none of the first five speakers are telling the truth, then both speaker 2) and speaker 4) are lying, so the number of truth-tellers among all six must be at least two. Contradiction.

• If two of the first five speakers are telling the truth, then it must be speaker 3) and speaker 5), so speaker 6) must be the third truth-teller, so speaker 6) must also say "Three of us are truth tellers". However, if speaker 6) does say this, then as far as the foreigner knows, it might be speaker 4) and nobody else telling the truth. This contradicts the assumption that speaker 6)'s statement is enough for the foreigner to know how many truth-tellers there are in total.

So exactly one of the first five speakers is telling the truth. That means speakers 2), 3), and 5) are lying, so the truth-teller among them must be either 1) or 4).

• If it's 1), then speaker 6) must be the second truth-teller, so speaker 6) must also say "Two of us are truth tellers". However, as before, if speaker 6) does say this, then as far as the foreigner knows, it might be speaker 4) and nobody else telling the truth. Contradiction.

So speaker 4) is telling the truth, which means

there is exactly one truth-teller in total.

Now what must speaker 6)'s response have been? It must be a lie, so it can't be "Only one of us is a truth-teller". It also can't be "Two of us are truth-tellers" (since then as far as the foreigner knows, it could have been speakers 1) and 6) telling the truth) or "Three of us are truth-tellers" (since then as far as the foreigner knows, it could have been speakers 3), 5) and 6) telling the truth). Any of the other options seems to be possible. So speaker 6) could have said

"None of us are truth-tellers" or "Four of us are truth-tellers" or "Five of us are truth-tellers" or "All of us are truth-tellers".