Knossos Games - Logic - Solution Three

solution

In the order of leaving the island:

Preston, Mary, Franklin, Madison, Chase,
Tiffany, Paul, Howard, Holliday, Russel, Clay,
Pearl, Chuck, Emory, Bill, ...

... and the winner: Eutaw

detailed solution

Holliday:

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

Holliday says she was one of the last five left, which cannot possibly be true, since if she was, she would have to be lying and thus couldn't have truthfully said the previous statement. That means she must have been one of the middle six (since that first statement is still a lie), and her next statement, that Mary was one of the first five kicked off, must be true.

Mary:

I was kicked off the island just after Preston.

Since Mary is one of the first five kicked off, her statement that she was kicked off the island just after Preston is true. At this point, it is not clear where in the first five she was kicked off, other than not first.

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 says she was not one of the middle six voted off the island. She thus cannot have been one of the last five off the island (which would make the statement true), and must either have been one of the first five, making both of her statements true, or one of the middle six, making her first statement false and her second statement true. In either case, her statement kicking off Franklin, herself, and Chase, in that order, is true.

Chase:

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

Chase states that she was kicked off after Mary. If this statement is false, she would therfore have been kicked off before Mary. But since Mary was one the first five kicked off, Chase would also be one of the first five kicked off, meaning she couldn't have made that false statement. Thus, this statement must be true.

Chase also states that she was not one of the last five to get kicked off of the island. This statement must also be true, because we just showed her first statement was true. If this statement was a lie, meaning she was one of the last five to be kicked off, then her first statement would also have to have been a lie, which it wasn't. (This also precludes the possibility of her being in the middle six. If the second statement was a lie, then she'd be saying that she was in the last five.)

Since both of these statements must be true, this forces Chase to have been one of the first five kicked off. With Franklin and Madison being kicked off before Chase, they must also have been kicked off within the first five. Thus, we have determined all five people who were kicked off in the first five. Finally, since Chase was kicked off after Mary, the order of the first five is set: Preston, Mary, Franklin, Madison, and Chase.

Next, let's see if we can seperate out the middle six (one true and one false statement) from the last five (all false statements). We've already established that Holliday is in the middle six. (Recap: Holliday says she was one of the last five left, which cannot be true, since if it is, she would have to lie and couldn't say that statement. That means she must have been one of the middle six, since that statement is still a lie.)

Preston:

Paul was kicked off the island in the middle six.

Preston, which we know was kicked out in the first five, states that Paul was kicked out in the middle six, which must be a true statement.

Russel:

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

Russel states that he was not one of the first five kicked out, which we know is a true statement. This means he must have been in the middle six (since he tells a true statement and was not one of the first five voted out).

Russel’s next statement is therefore false, so when he says that Tiffany was one of the last five kicked off, this forces Tiffany to have been kicked off in the middle six as well.

Howard:

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

Howard states that he was kicked off after Chase, which we know is true. Like Russel, this means that he must have been in the middle six (since he tells a true statement and was not one of the first five voted out).

Howard’s next statement is therefore false, so when he says that Clay was one of the last five kicked off, this forces Clay to have been kicked off in the middle six as well.

This makes Holliday, Paul, Russel, Tiffany, Howard, and Clay the middle six kicked off the island (in no particular order) and establishes that the remaining contestants, Emory, Bill, Chuck, Eutaw, and Pearl (again in no particular order), were the final five kicked off the island.

Preston:

Tiffany was kicked off before Paul.

Preston, who was kicked off in the first five and thus tells all true statements, says that Tiffany was kicked off before Paul.

Eutaw:

Howard was kicked off before Paul.

Eutaw, who was kicked off in the final five amd thus tells all false statements, says that Howard was kicked off before Paul, which means that Howard must have been kicked off after Paul, and thus also after Tiffany.

Emory:

Howard was kicked off after Holliday.

Emory, who was also kicked off in the final five and tells all false statements, says that Howard was kicked off after Holliday. This means that Holliday was actually kicked off after Howard, and thus after Tiffany and Paul too.

Chuck:

Holliday was kicked off after Russel.

Chuck, like Eutaw and Emory, was kicked off in the final five and tells all false statements, says that Holliday was kicked off after Russel. This means that Russel was really kicked off after Holliday, as well as Tiffany, Paul, and Howard.

Clay:

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

Clay states that he was kicked off before Madison, but this must be false because Madison was in the first five and Clay was in the middle six. That makes Clay’s other statement true, that he was kicked off after Russel, and thus also after Tiffany, Paul, Howard, and Holliday. Note that, while several of the above clues did not specifically state that a person was kicked off "just before" or "just after", and instead the more general "before" or "after", we now have determined the order of the middle six, based on the fact that there are only so many spots in the middle six available.

We have already established above that the final five are Emory, Bill, Chuck, Eutaw, and Pearl in no particular order.

Mary:

Pearl was kicked off before Chuck.

Mary, one of the first five kicked off and thus always tells true statements, says that Pearl was kicked off before Chuck.

Chuck:

I was kicked off after Emory.

Chuck, who is in the final five and thus tells all false statements, says that he was kicked off after Emory. This must mean that Emory was actually kicked off after Chuck, and thus also after Pearl.

Emory:

I was kicked off after Bill.

Emory, who is in the final five and thus tells all false statements, says that she was kicked off after Bill, which means that Bill was actually kicked off after Emory, and thus after Pearl and Chuck too.

Eutaw:

I was kicked off just before Bill.

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, as well as Pearl, Chuck, and Emory. This means Eutaw is the winner. Just as in the middle six, while several of the above clues did not specifically state that a person was kicked off "just before" or "just after" (espeically given the many false statements), we now have determined the order of the final five, based on the fact that there are only so many spots available.

First Posted : January 5, 2001
Last Updated : August 25, 2015

Knossos Games by Tim Boester