5 ms·

I'm not sure I get the setup of this puzzle. He tells you at the start that the total between between you is 18 or 20. So you know from the start that your frie

I'm not sure I get the setup of this puzzle. He tells you at the start that the total between between you is 18 or 20. So you know from the start that your friend sees 6 or 8 and she knows that you can see 10 or 12. So neither of you 'learn' that the other person sees at least 1 / fewer than 19 on the first round - you both already knew this. So what knowledge have you actually learned after the first round, that you can take forward into the second round?

CJefferson 8y ago
So, you don't know how many statues your friend can see. On day 1, imagine you go second. If your friend can see 19 or 20 statues, they know there is 20. Therefore, if you go second on the first day, you know your friend couldn't see 19 or 20 statues.
- sweezyjeezy 8y ago
  But you already know your friend sees 6 or 8 based on what you can see, and that you know that between you, you see 20. Both of you knew already, that this was not a possibility. I think I'm missing something from the setup.
  - yorwba 8y ago
    You know that your friend sees 6 or 8 and you know that if your friend sees 6 then they know you see 12 or 14 and (you know that they know that) if you see 14 then you know that they see 4 or 6 and (you know that they know that you know that) if they see 4 then they know that you see 14 or 16 and ((you know that they know that)^2) if you see 16 then you know that they see 2 or 4 and ((you know that they know that)^2 you know that) if they see 2 then they know that you see 16 or 18 and ((you know that they know that)^3) if you see 18 then you know that they see 0 or 2 and ((you know that they know that)^3 you know that) if they see 0 they know you see 18 or 20 ((you know that they know that)^4) if you see 20 then you know the correct answer and it's over So when it's not over on the first day, that updates your knowledge about each other's knowledge (about each other's knowledge ...) by eliminating that particular possibility. That goes on until only one possibility remains and you know the answer.
    - sweezyjeezy 8y ago
      Ah, nice. This is the answer I was looking for.
  - lucraft 8y ago
    This bugged me too, the process works but they’re throwing away a lot of information at the start, which should mean it can be done faster. I made another answer that works the same way but doesn’t throw that away, and it seems it’s possible to finish on Day 2.
OscarCunningham 8y ago
Good question. I suspect the answer is something like "that they know that you know that they know that you know that they see at least one statue".
falsedan 8y ago
> So what knowledge have you actually learned after the first round? That your friend sees 2 or more, and your friend knows you see 18 or less. By itself, this is trivially deducable; but each day walks the limits closer to revela a fact that isn't trivial. You start the puzzle knowning that your friend can see either 6 or 8 statues, and each day you add a new fact about how many statues she can't see. I'm more concerned that the problem as stated can be solved in 2 days: you say 18 on day one, then 20 on day two…
- 4ndr3vv 8y ago
  "Get it wrong, and neither of you ever leave. "
  - falsedan 8y ago
    Oh thanks, I missed this crucial caveat.
  - AstralStorm 8y ago
    Therefore you say I see more than (y - 2) statues while he says morethan (x + 2) until you both repeat the same value. You know you cannot lie so a simple iteration on inequalities is enough to find the right value. This relies on your friend figuring out the linear addition scheme.
- hav 8y ago
  Judging from: > [...] and so on, until you get it right or wrong. The caretaker cackles, “If you need me, I’ll be out preparing your graves.” My impression is that once you have the wrong answer, you're not going to have another day.

CJefferson 8y ago

So, you don't know how many statues your friend can see. On day 1, imagine you go second. If your friend can see 19 or 20 statues, they know there is 20. Therefore, if you go second on the first day, you know your friend couldn't see 19 or 20 statues.

sweezyjeezy 8y ago
But you already know your friend sees 6 or 8 based on what you can see, and that you know that between you, you see 20. Both of you knew already, that this was not a possibility. I think I'm missing something from the setup.
- yorwba 8y ago
  You know that your friend sees 6 or 8 and you know that if your friend sees 6 then they know you see 12 or 14 and (you know that they know that) if you see 14 then you know that they see 4 or 6 and (you know that they know that you know that) if they see 4 then they know that you see 14 or 16 and ((you know that they know that)^2) if you see 16 then you know that they see 2 or 4 and ((you know that they know that)^2 you know that) if they see 2 then they know that you see 16 or 18 and ((you know that they know that)^3) if you see 18 then you know that they see 0 or 2 and ((you know that they know that)^3 you know that) if they see 0 they know you see 18 or 20 ((you know that they know that)^4) if you see 20 then you know the correct answer and it's over So when it's not over on the first day, that updates your knowledge about each other's knowledge (about each other's knowledge ...) by eliminating that particular possibility. That goes on until only one possibility remains and you know the answer.
  - sweezyjeezy 8y ago
    Ah, nice. This is the answer I was looking for.
- lucraft 8y ago
  This bugged me too, the process works but they’re throwing away a lot of information at the start, which should mean it can be done faster. I made another answer that works the same way but doesn’t throw that away, and it seems it’s possible to finish on Day 2.

OscarCunningham 8y ago

Good question. I suspect the answer is something like "that they know that you know that they know that you know that they see at least one statue".

falsedan 8y ago

> So what knowledge have you actually learned after the first round? That your friend sees 2 or more, and your friend knows you see 18 or less. By itself, this is trivially deducable; but each day walks the limits closer to revela a fact that isn't trivial. You start the puzzle knowning that your friend can see either 6 or 8 statues, and each day you add a new fact about how many statues she can't see. I'm more concerned that the problem as stated can be solved in 2 days: you say 18 on day one, then 20 on day two…

4ndr3vv 8y ago
"Get it wrong, and neither of you ever leave. "
- falsedan 8y ago
  Oh thanks, I missed this crucial caveat.
- AstralStorm 8y ago
  Therefore you say I see more than (y - 2) statues while he says morethan (x + 2) until you both repeat the same value. You know you cannot lie so a simple iteration on inequalities is enough to find the right value. This relies on your friend figuring out the linear addition scheme.
hav 8y ago
Judging from: > [...] and so on, until you get it right or wrong. The caretaker cackles, “If you need me, I’ll be out preparing your graves.” My impression is that once you have the wrong answer, you're not going to have another day.