S2T2

Jim Randell 8:50 am on 12 November 2019 Permalink Reply
Tags: by: Dr V W Bryant ( 5 )   

• 

  Jim Randell 8:51 am on 12 November 2019 Permalink | Reply

  This Python program runs in 70ms.

  Run: [ @replit ]

  from enigma import (subsets, printf)
  
  # the possible behaviours:
  
  # T tells the truth
  def T(s):
    return bool(s)
  
  # F lies
  def F(s):
    return not s
  
  # U is unreliable
  def U(s):
    return True
  
  # honesty ratings
  honest = { F: 0, U: 1, T: 2 }
  
  # assign behaviours to A, B, G
  for (fA, fB, fG) in subsets((T, F, U), size=3, select="P"):
  
    # "B said A does not always tell the truth"
    if not fB(fA != T): continue
  
    # choose an age ordering for A, B, G
    for (aA, aB, aG) in subsets((0, 1, 2), size=3, select="P"):
  
      # "B said B was younger than A"
      if not fB(aB < aA): continue
  
      # "the younger of B and G said that A always told the truth"
      if not (fB if aB < aG else fG)(fA == T): continue
  
      # "A said that G said that A was older than B"
      if not fA(fG(aA > aB)): continue
  
      # map ages to behaviours
      m = dict(zip((aA, aB, aG), (fA, fB, fG)))
  
      # "the eldest said G was more honest than B"
      # "the youngest agreed G was more honest than B"
      s = (honest[fG] > honest[fB])
      if not (m[2](s) and m[0](s)): continue
  
      # output solution
      (A, B, G) = (x.__name__ for x in (fA, fB, fG))
      (a, b, g) = (["youngest", "middle", "eldest"][x] for x in (aA, aB, aG))
      printf("A={A}, {a}; B={B}, {b}; G={G}, {g}")
  

  Solution: Alpha is the eldest. Beta is the most honest.

  Alpha is the eldest, and sometimes tells the truth and sometimes lies.

  Beta is the middle, and always tells the truth.

  Gamma is the youngest, and always lies.

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