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Note: This was reposted from Knossos Games. I am not affiliated with the site in any way, shape, or form.

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Marooned on a tropical island.

Forced to send one fellow member of

their community home every few days.

Who will be the last to endure?

We caught up with some of the eight men (Clay, Preston, Paul, Russel, Chuck, Bill, Howard, & Franklin) and eight women (Tiffany, Pearl, Emory, Chase, Madison, Eutaw, Holliday, & Mary) who were stranded. Although they would not tell us who the winner was, they agreed to give us a few clues.

Unfortunately, they secretly agreed that, while the first five voted off the island would tell the truth, the middle six voted off would tell one true statement and one false statement each, and the last five removed would lie all the time. Is it possible, from their cryptic clues, to determine who was the last to remain?

Chase:

  • I was kicked out after Mary.
  • I was not one of the last five to get kicked off the island.

Eutaw:

  • Howard was kicked off before Paul.
  • I was kicked off just before Bill.

Russel:

  • Luckily, I was not one of the first five kicked out.
  • Tiffany was one of the last five kicked out.

Howard:

  • I was kicked off after Chase.
  • Clay was one of the last five to be kicked off.

Chuck:

  • Holliday was kicked off after Russel.
  • I was kicked off after Emory.

Preston:

  • Paul was kicked off the island in the middle six.
  • Tiffany was kicked off before Paul.

Holliday:

  • I was one of the last five left.
  • Mary was one of the first five kicked off.

Madison:

  • I was not one of the middle six to be kicked out.
  • I was kicked out just before Chase and just after Franklin.

Mary:

  • I was kicked off the island just after Preston.
  • Pearl was kicked off before Chuck.

Clay:

  • I was kicked off just before Madison.
  • I was kicked off after Russel.

Emory:

  • Howard was kicked off after Holliday.
  • I was kicked off after Bill.
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Here is my step by step.

I started with Madison. If her first statement is true then the second one must also be true. If the first statement is false, the second one must still be true. So the statement "I was kicked out just before Chase and just after Franklin." can be seen as a fact.

Next is Holiday. Her first statement "I was one of the last five left." is an obvious lies which forces her second statement "Mary was one of the first five kicked off." to be true.

Next is Mary. She was proved to be among the first five so all she says is true.

Next is Preston. He was proven to be before Mary so all he says is also true.

Next is Russel. His statement "Luckily, I was not one of the first five kicked out" cannot be a lie, and his second statement "Tiffany was one of the last five kicked out" is false, so he is in the middle 6.

Next is Clay. His first statement is false. Russel is in the middle 6 so if his second statement is false, he is also in the middle 6 and need 1 truth which is impossible, so his second statement must be true.

Next is Chuck. His first statement is a lie, his second one is still undetermined.

FACT LIST

- 16 - 5 liars - 6 both = top 5 is truth tellers.
- Madison was kicked out just before Chase and just after Franklin.
- Holiday is not first 5 but lied once so is in the middle 6.
- Mary was one of the first five kicked off.
- Mary was kicked off the island just after Preston.
- Pearl was kicked off before Chuck.
- Paul was kicked off the island in the middle 6.
- Tiffany was kicked off before Paul.
- Tiffany was not one of the last five kicked out.
- Russel is in the middle 6.
- Clay was kicked off after Russel.
- Clay is in the middle 6.
- Russel, Clay, Howard, Paul, Holiday, Tiffany(Tiffany is deduced to be in the middle 6 since Madison is the "delimiter" for top 5. If Tiffany was the delimiter, then Franklin would also have to be in the middle 6 and that would be 1 person too many.)
- Preston, Mary, Franklin, Madison needs to be top 5(1 missing).
- Pearl and Chuck are full liars(3 missing)
- Since Chuck's second statement is a lie, "Chuck was kicked off before Emory."
- Emory is one of the liars.
- Howard was kicked off before Holliday.
- Emory was kicked off before Bill.
- Bill is one of the liars.
- Eutaw says he was kicked just before Bill, so he is a liar but maybe not the last.

Resulting order from first to last :

Preston > Mary > Franklin > Madison > Chase > Tiffany > Paul > Howard > Holiday > Russel > Clay > Pearl > Chuck > Emory > Bill > (Eutaw?)

Conclusion

Either I made a mistake or this is impossible. Negating the statement that Eutaw was immediately before bill" does not imply he was after. If the statement was that he was somewhere before, then it would imply that he was after bill and therefore the last.

After consulting the original website.

The website offers the solution in details.
In the end, the author wrote this "Eutaw, who is in the final five and thus tells all false statements, says that she was kicked off just before Bill, which means that she was actually kicked off after Bill". Which I do not really agree with but... oh well...

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  • $\begingroup$ @suomynonA What answer are you expecting? Do you agree with the author's statement?(last part of my answer) $\endgroup$ – stack reader Jan 30 '17 at 4:21
  • $\begingroup$ Yeah, I came to the same conclusion. I found after searching Dr. Boester's blog that in the v7 update two people's statements were removed because they were redundant. I think the removal of the latter may have invalidated the solution inadvertently. "Paul: I was kicked off after Bill. I was kicked off before Russel. Tiffany: Holliday was kicked off before Paul. Emory was kicked off before Eutaw." The blog post. $\endgroup$ – Matthew0898 Jan 30 '17 at 5:08
  • $\begingroup$ @Matthew0898 Well, it's probably all just a big trap anyway. The last one is not kicked off the island since he is the winner haha. Maybe that's why Eutaw is stuck in a limbo and cannot be put anywhere. $\endgroup$ – stack reader Jan 30 '17 at 5:16
  • $\begingroup$ Yeah, I like that solution. Alternatively, Eutaw and Bill may have left at the same time, because they couldn't decide who to kick out. The original puzzle does work if you add Tiffany's statements back in though. $\endgroup$ – Matthew0898 Jan 30 '17 at 5:26
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In its current form it is not possible to determine whether Bill or Eutaw is the last person on the island. It is supposed to be Eutaw.

The last person is:

Either Bill or Eutaw. The positions of the first 11 people removed can be determined, but because the site where you found the puzzle was edited, there are four potential arrangements for the order of the last 5.

I will refer to the first five people to have left as being part of Group A, the 6th through 11th person to have left as Group B, and the 12th through 16th person to leave as Group C. Person 1 is the first person to have left, Person 16 is the last to have left. [X,Y,Z] indicates that that X left directly before Y, who left directly before Z.

It is stated that group A gives 2 true statements, group B gives 1 true statement and 1 false statement, and group C gives 2 false statements.

We therefore immediately know:

Russel is in group B because he states that he is not in group A. This statement must be true, because group A only gives true statements. If he was a member of Group A, his statement would be false. Since his first statement is true, he cannot be in group C either. He therefore must be in group B and his second statement must be false. This tells us that Tiffany must not be in group C.

Holliday is in group B because Holliday falsely states that she is in group C. If she was in group C, the statement would have been true, therefore preventing her from being in C. Since her first statement therefore must be false, she cannot be in group A. This also means that her second statement, that Mary is in group A must be true.

Mary then tells us that [Preston,Mary], which informs us that Preston is in group A.

As Preston is in group A, we know that Paul is in group B, and that Tiffany left before Paul. This tells us that Tiffany cannot be in C because Paul is in group B, and group C left after group B.

This is where it gets slightly more complex.

Chase tells us that Mary left before she did. This statement has to be true, because if it was false, she would have left before Mary, which would make her in group A. This excludes her from Group C. She then tells us that she is not in group C, which we already know to be true. This means that she is in group A, but that Mary left before she did. Madison must be in group A. If Madison's first statement(that she is not in B) was false, than her second statement would have to be true, because she would have to be in B. This means she cannot be in C, because that would make her first statement true, and nobody in C gives a true statement. This tells us that Madison is in A or B, and if she is in B, her first statement was the one that was false. This means that Madison's second statement has to be true. In her second statement, she tells us that she left just before Chase and just after Franklin.

With this, we know the name and order of the people who left in group A.

We know that Preston left immediately before Mary. We know that Mary left before Chase. We know that Franklin left immediately before Madison, who left immediately before Chase. So we know three things, 1. [Preston,Mary]

2. Mary before Chase. 3. [Franklin,Madison,Chase]

The order is

1. Preston

2. Mary

3. Franklin

4. Madison

5. Chase

We now know that:

given that nobody else told 2 true statements. Any of the remaining people who gave a true statement are in group B. The others are in group C. We already know that Russel, Holliday, and Paul are in group B. Tiffany must be in group B, because we already established she could not be in C, and A is full. Howard states that he left after Chase, and because this is true(we already know the names of the four people who left before Chase). Howard must be in group B, and his second statement must be false. Since he tells us that Clay is in group C, we know Clay is in group B.

We therefore know all of the members of Group B and all the members of Group C.

We know that the members of B are Russel, Holliday, Paul, Tiffany, Howard, and Clay. We know that the members of C are Pearl, Emory, Chuck, Bill, and Eutaw.

Knowing this, we can determine the order of B(though it isn't necessary to answer the question):

Eutaw is in group C, and her statement that Howard left before Paul must be false. This means that Paul left before Howard. Preston(group A) truthfully told us that Tiffany left before Paul. Chuck(group C)falsely stated that Holliday left after Russel. Clay's true statement was his second one, in which he told us that he left after Russel. Emory(Group C) falsely stated that Howard left after Holliday. This means that Tiffany left before Paul, who left before Howard, who left before Holliday, who left before Russel, who left before Clay.

This means the order so far is:

Group A:
1. Preston

2. Mary

3. Franklin

4. Madison

5. Chase

Group B:
6. Tiffany

7. Paul

8. Howard

9. Holliday

10. Russel

11. Clay

This leaves us with group C:

We already know the members of group C are Pearl, Emory, Chuck, Bill, and Eutaw. Eutaw's second statement (falsely) states that she left just before Bill. Chuck's second statement (falsely) states that he left after Emory. Emory's false statement is that she left after Bill. Mary(Group A) stated that Pearl left before Chuck.

This leads to the conclusion that:

This problem cannot be solved with only this given information. There are four potential ending orders. We know that Pearl is before Chuck, that Chuck is before Emory, and that Emory is before Bill, however all we know is that Eutaw did not leave immediately before Bill. This results in three potential solutions:

1. Eutaw left after Clay and before Pearl.

2. Eutaw left after Pearl and before Chuck.

3. Eutaw left after Chuck and before Emory.

4. Eutaw left after Bill.

In scenario 1-3, Bill is the last person to leave the island. In scenario 4. Eutaw is the last person to leave the island.

Extra information:

Once I came to this conclusion, I decided to check the website included along with the question. As it turns out, the author of the puzzle modified the puzzle(the original author, not the person who posted the puzzle here). It originally had 2 statements from Tiffany.
Tiffany:

  • Holliday was kicked off before Paul.

  • Emory was kicked off before Eutaw.
With this information, scenario 1-3 would have been eliminated, and Eutaw would have been the last person to leave the island.

This is because

Tiffany is a member of group B, and her first statement is false. The second statement therefore must be true.Emory must have left before Eutaw, and because Eutaw must not have left immediately before Bill, the only potential remaining spot would be after Bill.

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  • $\begingroup$ Yes, this puzzle is possible, I think with the modifications you mentioned at the end. $\endgroup$ – suomynonA Jan 30 '17 at 3:36
  • $\begingroup$ It is possible if you interpret Eutaw's "I was kicked off just before Bill" as meaning that Bill had to be kicked off after Eutaw(as the site you mentioned does in its "detailed solution") than the puzzle is possible. I don't know that this can in fact be assumed, because if Eutaw left two or three people before Bill, I would still think that it Eutaw's statement would count as false. That appears to be the logic the site uses to come to a conclusion. $\endgroup$ – Matthew0898 Jan 30 '17 at 3:48
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As we can see, there are only statements from 11 of the 16 castaways. Those who we hear from (Chase, Eutaw, Russel, Howard, Chuck, Preston, Holliday, Madison, Mary, Clay, Emory) and those we don't (Paul, Bill, Franklin, Tiffany, Pearl).

Let's start with Holliday's statements:

Holliday:
I was one of the last five left.
Mary was one of the first five kicked off.

If she was really in the last five, then she would tell all lies, but her first statement is clearly true, so she cannot be in the last five. Similarly, if she was in the first five, she must tell the truth and her first statement is clearly a lie, so she cannot be in the first five. Thus she is in the middle six. Her first statement is a lie, so her second statement must be true.

This tells us Mary was in the first five and is also telling the truth.

Here is our table of possibilities where their position ranges from 0-g (16 possible positions):

Clay     123456789abcdefg
Preston  123456789abcdefg
Paul     123456789abcdefg
Russel   123456789abcdefg
Chuck    123456789abcdefg
Bill     123456789abcdefg
Howard   123456789abcdefg
Franklin 123456789abcdefg
Tiffany  123456789abcdefg
Pearl    123456789abcdefg
Emory    123456789abcdefg
Chase    123456789abcdefg
Madison  123456789abcdefg
Eutaw    123456789abcdefg
Holliday      6789ab 
Mary     12345

Mary:
I was kicked off the island just after Preston.
Pearl was kicked off before Chuck.

So we know Preston was also in the first five and was before Mary. Also, Pearl came before Chuck. This isn't very helpful at the moment because it doesn't tell us much about Pearl or Chuck.

Clay     123456789abcdefg
Preston  1234
Paul     123456789abcdefg
Russel   123456789abcdefg
Chuck     23456789abcdefg
Bill     123456789abcdefg
Howard   123456789abcdefg
Franklin 123456789abcdefg
Tiffany  123456789abcdefg
Pearl    123456789abcdef
Emory    123456789abcdefg
Chase    123456789abcdefg
Madison  123456789abcdefg
Eutaw    123456789abcdefg
Holliday      6789ab 
Mary      2345

Preston:
Paul was kicked off the island in the middle six.
Tiffany was kicked off before Paul.

So Paul was in the middle six and Tiffany was definitely not in the last five since she was before him.

Clay     123456789abcdefg
Preston  1234
Paul           789ab
Russel   123456789abcdefg
Chuck     23456789abcdefg
Bill     123456789abcdefg
Howard   123456789abcdefg
Franklin 123456789abcdefg
Tiffany  123456789a
Pearl    123456789abcdef
Emory    123456789abcdefg
Chase    123456789abcdefg
Madison  123456789abcdefg
Eutaw    123456789abcdefg
Holliday      6789ab 
Mary      2345

Russel:
Luckily, I was not one of the first five kicked out.
Tiffany was one of the last five kicked out.

We know Russel cant be in the first five because of the immediate contradiction. Since his first statement is true, he also cannot be in the final five. Thus he is in the middle six and his second statement is false (we already knew that).

Clay     123456789abcdefg
Preston  1234
Paul           789ab
Russel        6789ab
Chuck     23456789abcdefg
Bill     123456789abcdefg
Howard   123456789abcdefg
Franklin 123456789abcdefg
Tiffany  123456789a
Pearl    123456789abcdef
Emory    123456789abcdefg
Chase    123456789abcdefg
Madison  123456789abcdefg
Eutaw    123456789abcdefg
Holliday      6789ab 
Mary      2345

Chase:
I was kicked out after Mary.
I was not one of the last five to get kicked off the island.

If Chase was in the last five she would have to lie, yet her first statement would be true (contradiction). If she was in the middle, her second statement is true so her first must be false and she must be kicked off before Mary. That would put her in the top five, so that is also a contradiction. Thus, she is in the top five and was kicked out after Mary.

Clay     123456789abcdefg
Preston  123
Paul           789ab
Russel        6789ab
Chuck     23456789abcdefg
Bill     123456789abcdefg
Howard   123456789abcdefg
Franklin 123456789abcdefg
Tiffany  123456789a
Pearl    123456789abcdef
Emory    123456789abcdefg
Chase      345
Madison  123456789abcdefg
Eutaw    123456789abcdefg
Holliday      6789ab 
Mary      234

Madison:
I was not one of the middle six to be kicked out.
I was kicked out just before Chase and just after Franklin.

Madison cannot be in the last 5 since her first statement would be true. If she was in the middle six, then her first statement is false making her second true. That would put her in the top 5 since Chase is in the top 5, so this is also a contradiction. Thus she is in the top 5 and this sets our top 5 places.

Clay          6789abcdefg
Preston  1
Paul           789ab
Russel        6789ab
Chuck          789abcdefg
Bill          6789abcdefg
Howard        6789abcdefg
Franklin   3
Tiffany       6789a
Pearl         6789abcdef
Emory         6789abcdefg
Chase        5
Madison     4
Eutaw         6789abcdefg
Holliday      6789ab 
Mary      2

Howard:
I was kicked off after Chase.
Clay was one of the last five to be kicked off.

We know Howard wasn't in the top five because those spots are taken. Since his first statement is true, he must be in the middle 6 and his second statement is a lie. Thus, Clay is also in the middle 6. Since that accounts for all 6 people in the middle, everyone else must be in the final 5.

Clay          6789ab
Preston  1
Paul           789ab
Russel        6789ab
Chuck                defg
Bill                cdefg
Howard        6789ab
Franklin   3
Tiffany       6789a
Pearl               cdef
Emory               cdefg
Chase        5
Madison     4
Eutaw               cdefg
Holliday      6789ab 
Mary      2

Now we can start compiling the orderings since we know the truth value of every statement.

Eutaw (lies):
- Paul before Howard - Bill before Eutaw
Chuck (lies):
- Holliday before Russel
- Chuck before Emory
Preston (true):
- Tiffany before Paul
Mary (true):
- Pearl before Chuck
Clay (1&1):
- Clay before Russel Emory (lies):
- Howard before Holliday
- Emory before Bill

So we get

Middle 6:
Tiffany < Paul < Howard < Holliday < Russel
Clay < Russel

Last 5:
Pearl < Chuck < Emory < Bill < Eutaw

So we know the winner was

Eutaw

but we don't know the full ordering because

Clay could have finished anywhere from 6th off to 10th.

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