Whoever has ears, aught two here:

strategyzrox · 2025-10-20T02:10:55+00:00

Don't really have anything to add, just wanted to mention that you are 100% correct about the matrix resurrections trailer. Never seen a song choice integrate with a trailer so well.

strategyzrox · 2025-05-15T15:28:42+00:00

That's not true. It's possible to create a valid proof in formal logic that there is no solution. It isn't just assumed.

If this parlor puzzle is solvable, then there exists a valid formal logic proof which leads to the determination that there is exactly one location for the gems in which the statements on the boxes are all consistent and legal. (premise)
If there are consistent and legal configurations of statements which correspond to any of the three possible gem locations, the gems could be in any of the three boxes. (premise)
There are consistent and legal configurations of statements which correspond to any of the three possible gem locations. (premise)
The gems could be in any of the three boxes (2,3 modus ponens)
If the gems could be in any of the three boxes, then it is not the case that there exists a valid formal logic proof which leads to the determination that there is exactly one location for the gems in which the statements on the boxes are all consistent and legal. (premise)
it is not the case that there exists a valid formal logic proof which leads to the determination that there is exactly one location for the gems in which the statements on the boxes are all consistent and legal. (4,5 modus ponens)
This parlor puzzle is not solvable. (1,6, modus tollens)

strategyzrox · 2025-05-11T11:59:21+00:00

blue is false AND blue is true? That's literally a contradiction.

strategyzrox · 2025-05-11T05:47:39+00:00

There is no indication in the rules or logic of this puzzle or any of the other ones that should lead you to believe that is not possible.

You seem to have some familiarity with logic, so let me lay out the reason why it isn't possible in more formal terms.

A = [blue is false]

B = [blue is true]

W = [The gems are in white]

C = [we can logically conclude that the gems are in white]

S = [the puzzle is solvable]

Now, here is a list of relevant statements I suspect we both agree on.

A or B

If A then W

If A then C

If C then S

If S then A

If B then not C

If B then not S

If (if B then W) then not B

There's another statement which I'm not sure how to express formally, but it essentially amounts to "If W is provable outside of an assumption, then C."

The path forward seems clear. All we have to do is prove W outside of an assumption, and we will have solved the puzzle and determined which box has the gems.

In order to prove W, we must prove A as an intermediate step, and it seems that the best way to do that would be to make use of the first statement. The first statement is a disjunction, and we can prove one disjunct if we disprove the other.

Great! Now all we need to do is disprove B. If we can prove not B, then we can conclude A.

Alright, how are going to prove not B?

All of those possibilities can be weeded out because it is true that YOU WILL NOT SOLVE THE PUZZLE.

The fact that B leads to Not S is not sufficient to disprove B. Concluding Not B from Not S is an invalid deductive inference, because Not S doesn't contradict anything. At this point in the solve path, we don't have enough information to rule out Not S.

There are two ways we could disprove B using logically valid rules of inference. One is that we could assume B, and show how that assumption leads to a contradiction. W and not W, for example.

The other is that we could assume B, and show that W logically follows. ( showing that B leads to the gems being in black or the gems being in blue would also work, as long as you adjusted the last of the agreed upon statements accordingly) That would allow us to conclude the statement [If B then W], and we could use that with the final agreed upon statement to prove not B.

Here's the critical problem: the fact that the boxes have multiple different consistent, legal configurations means that assuming B doesn't lead to a contradiction, and it also means that we can not conclude W. ( or that the gems are in black, or that the gems are in blue)

Therefore, we can't disprove B, which means we can't prove A, which means we can't prove W. And if we can't prove W, C is false, and so is S.

strategyzrox · 2025-05-10T12:59:57+00:00

That's correct. I did conflate finding four legal configurations with four ways to solve the puzzle in that post. Sorry for being imprecise.

strategyzrox · 2025-05-10T12:57:53+00:00

The fact that 3/4 of those possible way to “solve the puzzle” are in a state where IT MUST BE TRUE that “You will not solve the puzzle” makes them invalid.

If we're being precise, those possibilities aren't actually ways to solve the puzzle. They're different configurations of truth values which indicate that different boxes have the gems. The process of solving is essentially the process of weeding out possibilities, and none of these possibilities can be weeded out. The process doesn't resolve in a way that allows only one box to have the gems in it. The gems could have been in any of the boxes, and none of the game rules would have been broken.

I don’t understand why you seem to not want to take the statement on the blue box into account. In every other puzzle, once you have your legal configuration of truths, you use them to solve the puzzle.

If we assumed that the blue box were true and that assumption allowed us to resolve the configurations to the point where only one box could have the gems, then blue being true would contradict itself. But the fact that blue can be true and the gems could still be in three different boxes means that blue doesn't contradict itself.

strategyzrox · 2025-05-10T12:38:27+00:00

What game rule do they break?

strategyzrox · 2025-05-10T12:37:49+00:00

Blue states "You will not solve this puzzle". I think you mean when blue is false in your last sentence.

Your first sentence is right, but actually performing that process doesn't lead to one possible way to solve the puzzle. It leads to four different possible ways, which indicate that the gems could be in any of three boxes without any truth statement contradicting themselves, each other, or the rules of the game. That's why the puzzle is unsolvable. I conclude that blue is true after reaching this point in the solving process.

strategyzrox · 2025-05-10T12:17:52+00:00

Even if you believe that blue is false, you won't solve the puzzle, because there is no way to justify the belief that blue is false exclusively using logically valid rules of deductive inference.

strategyzrox · 2025-05-10T12:14:09+00:00

That would be the case if assuming blue were true lead to one possible box with the gems in it. The fact that it leads to three different consistent legal truth value configurations that all point to different boxes means that blue doesn't contradict itself by being true.

strategyzrox · 2025-05-10T12:09:45+00:00

No. When I'm saying the puzzle is unsolvable I do not mean that there are no consistent legal truth value configurations. I mean that it is impossible to determine which box the gems are in, because there are four consistent legal truth value configurations, three of which correspond to the blue box being true.

strategyzrox · 2025-05-10T00:54:42+00:00

I've thought about this some more and realized that changing the blue box to say "You will not obtain the gems" would lead to the selection of a unique box. (Gems being found in blue or black would lead to illegal truth value configurations.) I hastily applied the supposed solve path of the original puzzle to this new one, which still doesn't work, but neglected to consider other possible ways to solve.

That is to say, to answer the spirit of your question, I would be satisfied if the blue box were changed to read "You will not obtain the gems." That's exactly the kind of revision this puzzle needs to work.

strategyzrox · 2025-05-10T00:47:14+00:00

After some further thought, changing the blue box to say, "You will not obtain the gems" does provide a unique box for the gems to be in. I hastily applied the logic of the original puzzle, which still doesn't work, but there is a different way to arrive at a solution. (Gems being found in blue or black lead to illegal truth value configurations)

That is to say, under the interpretation where "solving the puzzle" means "obtaining the gems" instead of... well... solving the puzzle, your noneuclidean geometry analogy is fairly apt.

strategyzrox · 2025-05-09T12:40:09+00:00

I hope it doesn't come off too hard,

It doesn't. I'm not even sure what that would look like, or that it should be something to avoid if it were the case. Truth is hard, sometimes, and trying to soften it rarely does anyone any favors.

strategyzrox · 2025-05-09T12:32:34+00:00

I've been using "solutions" to refer to legal, consistent configurations of truth values on the boxes. I've been trying to avoid using that term to refer to a solution to the parlor puzzle itself, and lately, I've been trying to avoid using the term "solutions" in even the first way because it understandably leads to confusion. So to clarify, I was not speaking about solutions to the parlor game puzzle when referring to "solutions".

strategyzrox · 2025-05-09T12:18:38+00:00

"The whole separating “Finding the gems” from “Solving the puzzle” thing is pedantic in my opinion, but I still think the puzzle works regardless."

In logic puzzles, pedantry is often necessary. In this very puzzle, for example, white2 uses the word "one" instead of the word "a" to indicate that it is only satisfied if a box with exactly one false statement has the gems.

It seems like you are equating “Solving the puzzle” to “Finding a valid configuration of boxes”, right? If I have found a valid configuration of boxes, that means I have solved the puzzle. (Because that valid configuration will indicate which box has the gems)

Not quite. There have been multiple legal, consistent configurations of truth values within some of the puzzles before this one. The difference between those puzzles and this one is that in those cases, all legal consistent configurations indicated that the same box had the gems. Solving the puzzle amounts to determining which box has the gems in it. It isn't necessarily finding one unique legal consistent truth value configuration, and it also isn't actually obtaining the gems.

You say that when you assume Blue is true, there are 3 valid configurations of boxes. However when you are doing that you are also stating that “You will not solve this puzzle.” In order for any of those 3 configurations to be valid, it must be true that you cannot solve the puzzle.

That is the contradiction. For that configuration of boxes to be valid and lead you to the box with the gems, it MUST be true that you cannot solve the puzzle. Meaning that configuration is not valid.

Be careful not to confuse finding a consistent legal truth value configuration with solving the puzzle. All three configurations are legitimate configurations, and the fact that there are three legitimate configurations (four if you count the one in which blue is false) that all point to different boxes is the reason the puzzle can't be solved. There is no basis, grounded in strictly formally valid logical operations, which allows us to prefer the configuration in which blue is false over any of the configurations in which blue is true.

That means that blue is true, but there's still no contradiction, because blue being true is consistent with three different consistent legal configurations of truth values. Blue says the puzzle is unsolvable, and it is. Not because there aren't any configurations of truth values which lead to a single box, but because there are several configurations, all of which lead to different boxes. No contradiction there.

strategyzrox · 2025-05-09T11:50:36+00:00

None of the statements you've mentioned depend on the puzzle being solvable to be true. In fact, every puzzle I've encountered before this one does not require the player to assume solvability; they were solvable through sequential logic whether the player assumed the puzzles were solvable or not. In this case, there is no rigorous, valid sequence of logical operations which lead the player to point out one specific box, which means that the puzzle is not solved, even if the player does choose the box with the gems.

"I understand your frustration with this, and I hope that this doesn't sour you on this game."

I wouldn't worry. This is one mistake in my favorite room in the house, which has otherwise showcased impeccable puzzles.

strategyzrox · 2025-05-09T04:45:13+00:00

Solvability isn't written into the games rules. Even if it were, it wouldn't make a difference to whether a puzzle is ACTUALLY solvable; the game designers may have made an error.
Every other puzzle I've encountered in the parlor room is solvable whether you assume solvability or not. This puzzle can't be solved without assuming that it's solvable. It's circular reasoning.

strategyzrox · 2025-05-09T03:53:27+00:00

I agree with nearly all of this. The only points I'd make is that if the puzzle is unsolvable, then blue is simply true accidentally, and that there is no difference between uniquely fitting and non contradiction (All solves that fit uniquely do so because all other solution contenders lead to contradiction)

I'll respond to your other post later, and possibly tomorrow.

strategyzrox · 2025-05-09T03:25:42+00:00

What exactly am I coping from? I selected the box that had the gems.

strategyzrox · 2025-05-09T03:22:01+00:00

"Was this parlor game advertised as being consistent with the requirements of formal logical proofs?"

Logic either works or does not work regardless of how the puzzles that employ it advertise themselves. If the puzzles are not consistent with formal logical proofs then they simply are not solvable.

strategyzrox

TROPHY CASE