We get to choose what number we label each of the balls with, with no repeating numbers, correct? And we simply add the labels on any number of contiguous balls? And we label and arrange the balls such that for any number from 1 to 21, we can choose a set of contiguous balls from the “necklace” that add to 21? Anybody take a stab at this yet?
Edit: Wow it only just occurred to me that he’s talking about a literal set of billiard balls. That clarifies things a lot.
Yeah your interpretation of the riddle sounds correct to me, assuming you meant “that add to [that number]”.
Also I’m not sure that the numbers on the billiard balls need to be unique, unless we’re indeed picking from a single set of actual billiard balls, but it’s not very clear from the description above (I haven’t finished reading the chapter, maybe it’s clarified later).
So I just wrote a quick python script and found this:
Yeah after struggling with it a bit yesterday I realized the unique part might not have been specified, but that constraint seemed to make it more approachable analytically so I might have thrown it in there. The problem’s discussed a little in the beginning of chapter 3 (without an answer being given) which might clarify a bit? I didn’t click your spoiler tag yet—did your script give you an answer with unique numbers?
The only thing that makes sense to me is if they’re on the wrong side of the building. You could imagine the whole building rotating but I think that’s a bit far-fetched.
However, the building is symmetrical, so if they somehow (without realizing) exited through the north entrance instead of the south one and looked behind them, the building would look the same, provided the colors of the lights can be changed. If the planetarium room can slowly rotate, they could be tricked into thinking they’re going through the south exit but are actually facing north. Maybe the center platform doesn’t even move, it’s always the whole room that moves around it.
… HOWEVER, when they go back inside to move Ritsuko to her room, they would’ve realized if the building was the wrong way (they would need to turn left to go to the red building, not right as expected). It’s also mentioned that Moe looks around the entrance gate, and I’m not sure if there’s an identical looking one on the other side. Plus I think it’s hard to make the room (or building) move without people feeling any acceleration.
Yes I haven’t read your thoughts yet (in order not to spoil mine), so I will comment on yours later.
My thoughts on the disappearing statue
We had quite the setup with all the talk about magic and only being able to see what one allows oneself to see. This gap in human perception is exactly what magicians exploit, and the professor also seems to have exploited it.
Therefore my thought is that they were actually searching on the other side of the building.
In other words, the main hall was rotated while they were inside.
Here are some indicators for that:
The building is symmetrical, and the ground is also symmetrical. The colors of the two outer domes are only applied through illumination, and that could be switched easily. The outer domes’ interior including furniture is also identical. The furniture arrangement in the two lounges seems to have been different, but there could be an insider that helped with rearranging it.
During the show, the doors were blocked by the screens, therefore nobody could see what happened in the hallway (i.e. that it rotated).
The stage in the planetarium rotated. Once before they went outside, and once afterwards. But what if it was not the stage that rotated, but in fact everything else?
The weather was bad, and it was night. It was the same on the previous occurrence. This would keep anybody from accidentally spotting the statue that still stands on the other side of the building.
One tricky part is that Ritsuko collapsed and was taken back to her room. But what if it was not her room but in fact the identical room in the other building? That would be Noboru’s room. So it might well be possible that Noboru is the insider. On the other hand, Ritsuko is an actress, so she might be an insider as well. (Although that is less likely as she is directly related to one of the potential heirs and therefore biased. Noboru is not related to the family, therefore he would be better suited for the job.)
The key to Ritsuko’s room did not work was not available, and they had to use the master key. What if her key did not work Wouldn’t that nicely conceal the fact that Ritsuko‘s key wouldn’t have worked anyways because it was not her room after all?
We were notified of a vase with an exotic flower in “Ritsuko’s” room. I bet this will come in handy later, and that we will either learn that the vase was “taken” from Ritsuko’s room, or that Noboru’s room also contains such a vase.
Questions that remain:
How did Ritsuko get back to her room? Did she get back to her room after all, or was she in Noboru’s room while he showered? If she did get back, she could have walked over (if she was an insider) or she could have been carried over while unconscious (while the main hall rotated once more).
Do the rooms have labels attached to the doors? I am not sure about that point. It seems that the kitchen etc. don’t have labels, as Noboru explicitly had to show the kitchen to Moe, but what about the guest rooms in the other building? Did they have labels with numbers on them? I don’t remember.
Now we are waiting for the murder on the next day, I guess
@miwucGuess there is not much commenting required The only thing that bugs me a little bit: Isn’t that all too obvious? Can this really be the solution?? (especially compared to the solution in Subete and stuff…)
I’m honestly not sure if there was any mention of her key, just that the door didn’t open. To me it seemed like they didn’t have her key and immediately asked for the master key.
Indeed I think they were missing her key so they just used the master key. That would also explain why Ritsuko didn’t answer later on when her son knocked on the door, if she was in a different room. However, that means that Noboru’s room looks empty like a guest room, event hough he lives there (right?), I guess he’s just very neat and tidy?
Re furniture, somehow I thought they were different colors on both sides (blue/red) and I imagined matching carpet, but it seems I made all of that up. Re-reading, the hallways leading to each of the two sides have underfloor lights, as well as the circular paths around the lounges. And it’s explicitly said that the furniture is white but looks red/blue because of the lights. So then it’s super easy to swap. (and I really wasn’t paying enough attention).
Re labels on door, it’s not very clear. When Saikawa & Moe get to their room, it says 「すぐ右手の最初のドアが６号室だった」so I guess ６号 must be written somewhere. But maybe on the other side it’s also just labeled 1 to 6.
I still think you can’t move a whole room without people feeling any acceleration but because it’s a book they might get away with it.
I don’t think it’s very far-fetched. Slow accelerations (especially without visual reference) can be pretty much imperceptible (source: some trippy amusement park rides). Combine that with some good magician’s misdirection and I think it could make for a convincing illusion.
Hm, oh yes, I did not think about the fact that he is living there permanently. Well, if he really is an insider, then he may have prepared his room so that it looked like a guest room. For the why, he might have done that in order to make the others believe that the rooms are still the same. Of course he could not know that Ritsuko would collapse, but knowing her and her drinking habits, he might have helped a little bit (maybe by serving her extra strong alcohol? or drugging her a little? He was in charge of the drinks, after all…)
Re the acceleration, I was also thinking of something like amusement park special effects shows like @jhol mentioned. They also created a light show of the stars and stuff at the same time, so I was thinking when they rotate the stars, then it might be difficult to distinguish whether just the stars rotate or whether the building actually rotates. People might get dizzy enough from the rotation that these effects somehow overlap or feel like the same.
I was more wondering whether they would be able to start and stop the motion smoothly enough to make it imperceptible, but I guess it’s possible if enough money gets thrown at it.
When I read that passage, I thought about two different examples (they are not exactly the same but somehow related, I think).
The first is a very old attraction (I think it existed in the 80’s already); it is a dome where a video gets projected from the inside. People would just stand inside (on the concrete floor) and watch the video. Usually the video has a shock-effect like e.g. I once watched a helicopter flight over the Grand Canyon or something, filmed from the helicopter down. First you would see the top of the cliff, and then all of a sudden the helicopter would fly across the edge of the cliff and you look down like 1000 meters or so. There are usually a few people that fall down onto the ground (on their own, just from watching) because the brain somehow reacts to the visuals and forces the body to move in order to counter-balance a movement that is not actually there, which leads to them falling. So here you have bodily reactions without actual movement, which is sort of the inverse of our case.
The second one is much more technically sophisticated and newer (I think it came out in the mid-90’s); it is also a dome, and people get to sit in a little cart (maybe 6 rows of 4 people each or a bit larger) inside the dome. This cart is being moved in a super-precise way to match up the scene that is projected onto the dome. In my case it was a dystopian roller-coaster ride through open space, with the roller-coaster cart leaving the (broken) tracks, flying through the air and landing on the tracks on the other side of the gap, etc. It felt so realistic to me that it took me a few minutes to realize that we did not actually move at all, and I only realized because there was no wind from the movement
Today I also remembered this phenomenon when you sit in a train that stands in a train station, and sometimes when the neighbor train would start to leave the train station, it sometimes feels to me as if my own train started moving and we are going in the opposite direction.
In all these three cases visuals are strong enough to “override” bodily sensations (or the lack thereof). Especially the last example makes me think that if we think that the train moved although it did not move, then its real movement must be so subtle that we usually don’t notice it at all. (At least for the first few meters.)
Back to our scene with the rotating main hall: If the visuals are strong enough (e.g. the sky is rotating as well) I guess that might override any real movement we are experiencing, thus leaving us with the impression that it was “just the rotating projection”.
This calls for an interesting experiment: If you close your eyes and plug your ears, will you notice whether a train starts moving? (Given it is a high-speed train with good cushioning and stuff, not a simple tram.) I’m not sure I would…
Thanks for the super detailed answer! I’ve never been in any rides like that. I still feel like most of this is different from the issue at hand, but you might be right, when a high-speed train (like the TGVs we have in France) starts slowly, it’s actually pretty smooth and might not be that noticeable.
Well, at least the identity of the 笑わない数学者 is pretty clear by now
When the planetarium started to rotate and the screens blocked the doors (and the 北, 東 etc plates above them) I was like “ok the execution of the “making everybody lose their sense of correction” trick seems even easier than I expected”! But then complications arise, namely:
and
I’m still waiting for them to enter Ritsuko’s actual room and her not being there… but the gate thing is a problem. The only solution would be an identical gate and enough fog to conceal the outside surroundings. But surely someone living there / being there frequently would know of such a thing.
But that would make Noboru the murderer? (Or he is simply in on the statue trick?). Because otherwise surely he would have recognized his own room. But Shun’ichi definitely seems to have some sort of problem with him, so that’s a possible motive. And drugging Ritsuko isn’t all that difficult either as the barkeeper. She also always stays in the same room, which makes everything predictable.
I actually thought that Shun’ichi and Ritsuko shared a room at first (like Moe and Saikawa), and was thinking “surely Shun’ichi would notice if they were in the wrong room?” But looking at the layout of the building again (conveniently with names and all), they don’t.
I haven’t read your thoughts yet (in order not to spoil mine), so I will comment on yours later.
The only thing that bugs me a little bit: Isn’t that all too obvious? Can this really be the solution?? (especially compared to the solution in Subete and stuff…)
