Oddbean new post about login | logout OK, it's a bit underspecified 😄 Say the opponent/challenger also gives a full list of answers to both sets of 1000 questions - but only for 2 or 3 minutes, after which you lose access. Given that, what protocol could you devise that would convince him that you basically already knew all 1000 answers for 1 of the 2? But not revealing which?
say you know the answer to all the questions you're asking, and that you can trust him to do operations honestly. As a grug brain I'd say : 1000questions aboutlizards 1000 questions about math guy. he, in secret scores his own answers based on the answers I give him. The gives me the total score of both. He's going to say : I have 2 lists, to which I have a score of 750 to one of them and 200 to the other.
I don't follow what you're saying. There's one person claiming to be expert in (komodo OR fermat). There's another, providing the 2 lists of Qs and, for a very limited time, answers. You can assume that the first person is indeed enough of an expert in one of the 2, that they can easily correctly answer all 1000.
Ok I understand. Simple : You put the expert in a room with a locked box. The box opens with one of 2 combinations. Inside is a gem. The combination to open the box is : the first letter of every answer of either lists. so it's a 1000 letter combination. 2 possible combinations. He just needs to go in the room and come out with the gem. If he does he's an expert in either lizards or old math dudes. Does that work ?
Nice answer :) It's a slightly more fun version of, e.g. having a computer program that asks you to enter correct answers and prints out pass/fail, so basically you answer the questions in secret and the challenger sees only the result, and believes that it was executed correctly ... which is pretty reasonable. (not the intended answer of course; for that no mechanical or digital mechanisms needed).
So I thought about it more. If no machines are allowed, can't we just craft 2 lists of questions whose answers add up, in total, to a certain number of letters. The same sum for both lists. The expert reads the questions and gives the total. If the total is ok, he knows, if not, he doesn't?
Really interesting idea, I like it. Obviously difficult in practice, but the spirit of the idea makes sense, as long as the numbers get large enough.
Ok, I give up, 😭😭😭. What's the answer ?
No, you succeeded I'd say, that last idea feels like a valid solution ... unless i missed something. I'll post the 'intended' answer later.
Answer at nostr:nevent1qqs8pa4xuat4ukptmgj70jc56p609uv8mv5aja0q242ug5p9mtv2zqcpr4mhxue69uhkummnw3ezucnfw33k76twv4ezuum0vd5kzmp0qgsxwkuyle67y94tj378gw8w2xw2wa6nwmwlqhddlwnz0z7sztsaw2qrqsqqqqqpm4sw7n @AbstractEquilibrium ping also
What's the definition of success? The opponent gleans on which topic the player has expert knowledge? Or the player convinces the opponent that they have full knowledge of both? In a vacuum, I'd say the protocol would be to lock both players in a room until only one remains, but I sense that's not the essence of what you're asking 🤣
Does the opponent know which answers the player accesses? At what rate can the player digest the answers they didn't already know? Can the protocol still be successful if for some reason the player provides an incorrect answer in both lists?
1. No. 2. I think we could be vague on this, but let's keep it concrete: there's only time to memorize 1 answer. 3. In the 'correct' answer to this puzzle, no. Good questions.
If I'm the opponent demanding the proof of expertise of one of the two areas, I would start asking questions from *one* of the lists, offering 1 (or n) answers if requested by the player, up until they reach the quota. If the player completes the first 1000 questions, they win. If the player ever provides an incorrect answer, the round ends. Next round, I start asking questions from the second list, continuting the quota of freebies from before. Same rules. If the player completes the second 1000 questions, they win. If the player ever provides an incorrect answer, the game ends. I don't see a way to conclude the game without asking 2000 questions, or the player failing early. I'm curious 🙂
Okay reading nostr:nprofile1qqsyzrawlu9t7hta0sszkn6zuvqndgcwm49wk6eckxtjk6lhgtyly6cppemhxue69uhkummn9ekx7mp0qyfhwumn8ghj7mmxve3ksctfdch8qatz9uq3samnwvaz7tmjv4kxz7fwvd6hyun9de6zuenedyhs4xywes think it through, I suppose an encoding of the answers (full knowledge) could be formed by the expert. I'm not sure how the encoding scheme would be communicated between the player & the challenger, because it's outside of the game
Simpler answer, I guess I keep coming up with variations : 2 lists : multiple choice for each question. The catch is that the sequence of good answers is the same in the two lists : like a,c,d,d,b..... The expert just returns 2 sequences of 1000 letters. If he is an expert, one of those two are correct, if not he's craig wright ?
Yeah basically variants on 'the two answer sets can be 'encoded' and are chosen to have an identical encoding'. But can you find a way to do it that doesn't require answering a thousand questions? Based on the concept that, if one were challenged to answer one specific question randomly, one is guaranteed to succeed based on knowing all the answers?
The word 'random' makes me think "no" We'd have to preindex the set of questions, which necessitates evaluating all of them.
"I have a 5000 word dictionary, and insert 5 of the words into a database. Can I then randomly query the database for any of the 5000 words, and be guaranteed a result?" No. Your odds are literally one in a thousand 😉
I keep thinking, but best I can do is probalisitically get there. I don't see how I can be convinced he's an expert UNLESS he answers all the questions correctly. I can be more and more sure that he is, but never convinced. I'm probably missing something.
💯 (I rounded up)
Gotcha, so yeah, the player will need to evaluate & answer at least 1000 questions, the set that they know, to combine them into a unified result. After that, sounds like a matter of privacy for the player as they consider how to combine their knowledge into a single value. Is that a single play, or can the opponent react at each step? Cool problem!