I'm still completely baffled after a couple of dozen rolls. The only progress I've made is being able to rule out two classes of rules, one based on observation of unchanging form of question, and another based on the fact that it's original based on the cast of dice.
I cheated and googled too. Found a hint with an alternative name for the game and realized what it was about. I don't know how long it would have taken me without that, but a very long time - I was trying much too complicated rules along completely the wrong lines.
Interesting supplementary question - when you assumed you had got it right, how many further attempts did you take before you believed firmly that your rule was the correct one? We're all assuming that a certain level of induction gives us the right to believe we've solved the puzzle, because there's no solution given by the author. The actual rule might be "the answer is produced by rule R1 unless the number of guesses so far is a multiple of 100, in which case use rule R2".
Even so, there could be other rules which just happen to produce the same sequence of numbers, especially if you've come up with the solution in a short number of "throws" and only done a small number to "confirm". Since nobody's stating what their solution is, it's conceivable that some of the people who say they have solved it are thinking of different rules.
I saw this many months ago. I can't remember exactly how long it took me to get the answer, but it can't have been more than a handful of throws.
The question was so strange that I could see no alternative but to regard it as a clue.
As for how I decided my answer was correct, having made the statelessness assumption, I tested a couple of dozen more throws, making sure I'd seen all possible numbers of pips on a die face go past semi-independently in several positions. Since the answer is simply the summation of the independent scores for each die, and the rationale for the answer is so clear given the clue, not much further checking is needed.
That I think is the most meaningful question. I figured out a rule after the first answer, (working verbally rather than mathematically). Then I tested my rule three times and was correct. Was just about to give up and comment here 'yup, got it straight away' when I got a fourth wrong. And that fourth throw allowed me to deduce the correct rule, though having got it wrong once I ended up making quite a lot of tests before I was convinced.
The statistical oddity was that I didn't throw a single 3 in any of my first four tests. I didn't realize until afterwards that this had skewed my reading of the game, though.
Most of the other versions of this on the web include the note that the title is important as an explicit part of the instructions, which I agree makes it easier. (Without that, I find this (kind of) puzzle really irritating -- it's like the puzzle-setter is breaking an implied contract with the puzzle-solver.)
Only took me three. Though I'm not sure whether to count the first one, since the script failed to print a number at all! (I later figured out why this was, though, so it did turn into a data point in the end.)
I really don't like the style of things like this. No objection to this sort of puzzle, merely the presentation of puzzles as hazing rituals where the answers are to be kept secret. (*) If you're looking for inductive logic puzzles, try Bongard Problems (http://www.cs.indiana.edu/~hfoundal/research.html), or play Zendo (http://www.wunderland.com/WTS/Kory/Games/Zendo/).
(*) This is why the chairman's game provokes such an emotional reaction from me. Bah.
This is why the chairman's game provokes such an emotional reaction from me.
But in which direction is this reaction? I believe you have stated that you are not averse to the occasional chairmanly game, which seems to be in contradiction with your objection to "hazing rituals where the answers are to be kept secret". Or maybe that was your point.
Got it from the answer to the first roll. My first six guesses were all "4", and the latter five were all correct! [ small integer statistics strike again ]
Am trying to ignore the "more intelligent -> longer to get it" bit, as it's rare enough that I do manage to leap to the correct answer in puzzles.
I suspect that it does a moderately good job of partitioning people who are more linguistic puzzle vs logical/numerical/topological puzzle oriented, by looking like a numeric/logical puzzle, but actually having a significantly lingustic component.
And I'm even more baffled having read j4's hint and everyone else's comments on the same line -- I'd assumed the title/question was a hint, but couldn't come up with anything based on it that might work, so abandonned it for other lines of attack.
I'd been trying to work out whether the middle tile might be the rose and the others around it the petals, (alternatively the middle three as the rose and the other two as the petals) but that doesn't seem to work. I don't think there's any division involved since there's always a whole number of petals, but beyond that I haven't got a clue.
That's the kind of thing I threw out on the basis of it originally being done with dice. (Although that has the assumption that the question is asked with the dice lying as they fell, rather than with them rearranged into a line.)
I got a connection refused, so sod it, I'll just mention that a long time ago the great Martin Gardner described a card game where one person thinks of a rule for laying down cards in sequence, and the others try to play the cards: 'God' tells them if it's an legal play. First one to suss the rule will obviously get rid of all their cards first and win, modulo a bit of luck with the deal.
"Eleusis". I've played it. It's quite fun; lets you do the inductive reasoning stuff in a less chaotic environment than Mao.
Best thing about it, I think, is the scoring mechanism, in which the "God" player's score is determined by the spread of the other players' scores (those in turn being basically determined by how long it took them to guess the rule and hence stop making errors). This gives God an incentive to tailor his rule to the skill level of the players, so that some people will get it quickly and others will take longer; rules that are too easy or too hard don't score as highly.
Hmm, this sounds like the devious "God" would make up a rule of the form "Player 1 may play any card he likes, but player n may only play the nine of diamonds."
I assume it is specified somewhere that the rules must be player-independent.
I assume so, although it's a long time since I read the formal rules. The group I played with had a clear understanding of the intent of the game and were more interested in playing it sensibly than in trying to find the loopholes...
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(no subject)
Date: 2004-09-21 09:53 am (UTC)Guessed what kind of rule it would be on the first roll, but took a few more to work out exactly what it was. (Gur gvgyr tvirf vg njnl!)
(no subject)
Date: 2004-09-21 10:08 am (UTC)(no subject)
Date: 2004-09-21 10:01 am (UTC)(no subject)
Date: 2004-09-21 10:32 am (UTC)(no subject)
Date: 2004-09-21 12:51 pm (UTC)(no subject)
Date: 2004-09-21 10:02 am (UTC)(no subject)
Date: 2004-09-21 01:12 pm (UTC)(no subject)
Date: 2004-09-21 10:07 am (UTC)(no subject)
Date: 2004-09-21 10:08 am (UTC)(no subject)
Date: 2004-09-21 10:09 am (UTC)(no subject)
Date: 2004-09-21 10:19 am (UTC)(no subject)
Date: 2004-09-21 10:37 am (UTC)(no subject)
Date: 2004-09-21 11:58 am (UTC)(no subject)
Date: 2004-09-21 12:28 pm (UTC)(no subject)
Date: 2004-09-21 01:19 pm (UTC)The question was so strange that I could see no alternative but to regard it as a clue.
As for how I decided my answer was correct, having made the statelessness assumption, I tested a couple of dozen more throws, making sure I'd seen all possible numbers of pips on a die face go past semi-independently in several positions. Since the answer is simply the summation of the independent scores for each die, and the rationale for the answer is so clear given the clue, not much further checking is needed.
(no subject)
Date: 2004-09-22 03:03 am (UTC)Or something.
(no subject)
Date: 2004-09-22 07:49 am (UTC)The statistical oddity was that I didn't throw a single 3 in any of my first four tests. I didn't realize until afterwards that this had skewed my reading of the game, though.
(no subject)
Date: 2004-09-21 10:51 am (UTC)(no subject)
Date: 2004-09-21 11:27 am (UTC)(no subject)
Date: 2004-09-21 12:22 pm (UTC)Most of the other versions of this on the web include the note that the title is important as an explicit part of the instructions, which I agree makes it easier. (Without that, I find this (kind of) puzzle really irritating -- it's like the puzzle-setter is breaking an implied contract with the puzzle-solver.)
(no subject)
Date: 2004-09-21 11:04 am (UTC)(no subject)
Date: 2004-09-21 11:22 am (UTC)(no subject)
Date: 2004-09-21 11:28 am (UTC)(no subject)
Date: 2004-09-21 01:24 pm (UTC)I really don't like the style of things like this. No objection to this sort of puzzle, merely the presentation of puzzles as hazing rituals where the answers are to be kept secret. (*) If you're looking for inductive logic puzzles, try Bongard Problems (http://www.cs.indiana.edu/~hfoundal/research.html), or play Zendo (http://www.wunderland.com/WTS/Kory/Games/Zendo/).
(*) This is why the chairman's game provokes such an emotional reaction from me. Bah.
(no subject)
Date: 2004-09-21 03:59 pm (UTC)But in which direction is this reaction? I believe you have stated that you are not averse to the occasional chairmanly game, which seems to be in contradiction with your objection to "hazing rituals where the answers are to be kept secret". Or maybe that was your point.
It took me about 7 rolls, incidentally.
(no subject)
Date: 2004-09-22 08:45 am (UTC)(no subject)
Date: 2004-09-21 02:22 pm (UTC)(no subject)
Date: 2004-09-21 03:15 pm (UTC)(no subject)
Date: 2004-09-21 03:41 pm (UTC)Am trying to ignore the "more intelligent -> longer to get it" bit, as it's rare enough that I do manage to leap to the correct answer in puzzles.
I suspect that it does a moderately good job of partitioning people who are more linguistic puzzle vs logical/numerical/topological puzzle oriented, by looking like a numeric/logical puzzle, but actually having a significantly lingustic component.
(no subject)
Date: 2004-09-21 04:11 pm (UTC)(no subject)
Date: 2004-09-21 04:53 pm (UTC)(no subject)
Date: 2004-09-22 02:03 am (UTC)And I'm even more baffled having read
(no subject)
Date: 2004-09-22 02:11 am (UTC)And one of the rules I'd discarded yesterday appears to be correct. Ho hum.
(no subject)
Date: 2004-09-22 05:12 am (UTC)(no subject)
Date: 2004-09-22 05:54 am (UTC)That's the kind of thing I threw out on the basis of it originally being done with dice. (Although that has the assumption that the question is asked with the dice lying as they fell, rather than with them rearranged into a line.)
(no subject)
Date: 2004-09-22 01:39 am (UTC)(no subject)
Date: 2004-09-22 02:18 am (UTC)(no subject)
Date: 2004-09-22 03:57 am (UTC)Best thing about it, I think, is the scoring mechanism, in which the "God" player's score is determined by the spread of the other players' scores (those in turn being basically determined by how long it took them to guess the rule and hence stop making errors). This gives God an incentive to tailor his rule to the skill level of the players, so that some people will get it quickly and others will take longer; rules that are too easy or too hard don't score as highly.
(no subject)
Date: 2004-09-22 04:14 am (UTC)I assume it is specified somewhere that the rules must be player-independent.
(no subject)
Date: 2004-09-22 04:35 am (UTC)