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Molson_Hart's profile
Molson Hart
Molson Hart
Molson Hart
@Molson_Hart

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Molson Hart

@Molson_Hart

CEO at http://amazon.com/viahart . CEO at http://edisonlf.com . I tweet about business, e-commerce, supply chain, health, law, & infrastructure

Austin, TX
Joined July 2015

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    1. Joe Shipman‏ @joe_shipman Jun 9
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      Joe Shipman Retweeted Joe Shipman

      Still not getting anyone trying this. In one of the comments I showed how a proof for k=3 goes. Hint for general case: pick a sequence of 2k-2 people using a “majority” criterion and show that within the sequence is a k-clique or a k-anticlique.https://twitter.com/joe_shipman/status/1270123256637505536 …

      Joe Shipman added,

      Joe Shipman @joe_shipman
      NEW MATH PUZZLE Previous one was too hard, answer posted. Prove that if there are at least 2^(2k-3) people at a party, there are either k people who all know each other or k people who are all strangers to each other. (Assume symmetry, if you know someone then they know you.)
      Show this thread
      2 replies 0 retweets 1 like
      Show this thread
    2. Molson Hart‏ @Molson_Hart Jun 9
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      Replying to @joe_shipman

      Stupid question probably but I can’t figure it out. If k = 3 I need to show that at a party of 8 or more, either 3 people all know each other or 3 people don’t know each other at all? Why can’t 8 people not know each other?

      1 reply 0 retweets 0 likes
    3. Mallrat9000‏ @Mallrat9000 Jun 9
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      Replying to @Molson_Hart @joe_shipman

      The question says one of two conditions must be true (3 people are all mutual friends, or 3 people are all mutual strangers). In your example, if 8 people are all mutual strangers, then certainly any 3 of them are as well. So the second condition is true.

      1 reply 0 retweets 1 like
    4. Mallrat9000‏ @Mallrat9000 Jun 9
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      Replying to @Mallrat9000 @Molson_Hart @joe_shipman

      Another way to state the problem: in a group of 8 people, it can’t be the case that every combination of 3 of them has at least one pair of friends and one pair of strangers.

      2 replies 0 retweets 1 like
      Molson Hart‏ @Molson_Hart Jun 9
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      Replying to @Mallrat9000 @joe_shipman

      Thank you.

      8:32 PM - 9 Jun 2020
      0 replies 0 retweets 0 likes

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