plainglazed
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Everything posted by plainglazed
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the above is mostly to purge that thought and to let you know am on the case. will still be pondering this one and hope you let it go a little longer.
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I think the added bit of information that allows us to make positive conclusions is the fact that truthtellers are a majority.
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For the general case it is not a stretch that the above quote in red could also read, "troublemakers can not be a majority of the 2nd members of each pair after eliminating any pairs that have responded "no". Eliminating pairs responding "no" either drops a troublemaker and a truthteller or drops two troublemakers. In both cases this just further promotes the truthtellers as the majority. So with 99 villagers, after 49 questions, consider the worst case where all respond "yes". As Nana7 did, let's collectively call those asking if another is a truthteller the 1st members and those being inquired about the 2nd members. There is obviously a maximum of 49 troublemakers in the 1st members. But in this case, the corresponding members of the second group all must be truthtellers (a clear cut majority which is what we want to prove). Each truthteller swapped with a troublemaker of the 49 1st members puts a corresponding truthteller in the group of second members thus maintaing a majority of truthtellers in that group. When the group of 1st members consists of 24 truthtellers (or more) and 25 troublemakers, the group of 49 2nd members consists of at most 24 troublemakers. So the group of 49 second members always has a majority of truthtellers irregardless of the 99th villager. We can now take the group of 49 second members with an established majority of truthtellers and repeat the process. For less than $100 we can establish a truthteller. A most excellent puzzle hahaputao!
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It's not so much that I hate cats, it's just that I like chicks more.
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also like Wilson's - as usual. but just in case...
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Letter Exchange - most responses
plainglazed replied to peace*out's question in New Logic/Math Puzzles
Unfortunately, that ATTACK was a little too little and a little too LATE. -
me too. had me stumped . a most excellent riddle TheSilencer!
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I have an idea but am still contemplating...
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But wouldn't they actually likely be still in bed? I'm like a leaf, when you see my backside you know... the wind is blowing.
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Kudos to thoughtfulfellow, k-man, and harpuzzler. k-man gets top marks for stating the distance is a constant as is easily proved by comparing the area of the entire equilateral triangle to the three triangles formed by connecting the random interior point to each vertex of the original triangle. For the general case of an equilateral triangle ABC of side length s, the area = sqrt(3)s2/4 and the sum of the areas of triangles ACK, CBK, BAK = s/2(h1+h2+h3). Equating the two yields h1+h2+h3=sqrt(3)s/2.
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If you were a rose you would still be a thorn in my side.
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When I turned on the lights in our triangularly shaped dog den I noticed what I think is a previously undiscovered survival technigue of the common cockroach. Three such vermin had been feasting on a piece of kibble but as soon as the light came on they all scattered, keeping both maximum distance from one another and taking the shortest straight line path to the edges of the pen where they quickly discovered some crack and made their escape. Quite fantastic, really. But then I wondered, if the pen has uniform side length of 2 meters, what is the expected average total distance the three pests travel given that piece of kibble could be anywhere within the den?
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Letter Exchange - most responses
plainglazed replied to peace*out's question in New Logic/Math Puzzles
I think the rules kinda evolved. At some point (curr3nt maybe?) changed one letter, added a letter, or dropped a letter as per the OP but made two words as a result. For some time there had been some back and forth between two and one word answers while keeping within the rules of either changing, dropping or adding a letter to the previous word(s). I had pushed it to three words by adding K to LACTATE making LACK and TATE and dropping R from BRAN making BAN as LACTATE BRAN seemed to be a dead end. Hope it gets back to two words shortly. She came BACK and ATE AN awfully old egg salad sandwich. -
I'm always right when there's nothing left.
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I never get drunk friends to drive me home.
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yeah, really liked shakingdavid's answer and thought he might have had it. been thinking on this one on and off for weeks...
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gotta go with the majority opinion. up to you, maurice.
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