S2T2

Jim Randell 8:26 am on 9 July 2019 Permalink Reply
Tags: by: B W M Young ( 10 )   

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  Jim Randell 8:28 am on 9 July 2019 Permalink | Reply

  This Python program runs in 81ms.

  Run: [ @replit ]

  from enigma import (subsets, printf)
  
  # the behaviours of the computers
  def F(s): return (not s)
  def U(s): return True
  def T(s): return bool(s)
  
  # the professor asks two of the computers (identified by size)
  for (a, b) in subsets((0, 1, 2), size=2):
  
    # record largest computers in scenarios that work
    rs = set()
  
    # consider all possible size orders (L, M, S)
    for size in subsets((F, U, T), size=3, select='P'):
      (L, A, B) = (size[0], size[a], size[b])
  
      # first computer states "1969 (T) is largest"
      if not A(L == T): continue
  
      # second computer states "1960 (F) is not largest"
      if not B(L != F): continue
  
      rs.add(L)
  
    # look for unique solutions
    if len(rs) == 1:
      L = rs.pop()
      printf("L={L.__name__} [a={a} b={b}]")
  

  Solution: The largest computer is from 1965.

  So the largest computer, from 1965, is unreliable.

  The medium sized computer is from 1960, and always makes false statements.

  The smallest computer is from 1969, and always makes true statements.

  The Professor asks his first question to the medium sized computer, and his second question to the smallest computer.

  ---

  We can verify manually that this does indeed give a solution.

  First we refer to the computers by their behaviour, instead of their year. So:

  1960, always makes false statements = F
  1965, makes unreliable statements = U
  1969, always makes true statements = T

  The Professor asks the firsts question (“which computer is largest”) to M (the medium sized computer), and gets an answer of “T”, and he then asks the same question to S (the smallest computer), and gets an answer of “not F”.

  There are six possible orders of computer (Largest, Medium, Smallest):

  L=F, M=U, S=T: S would not say “not F” (as S=T and L=F). Impossible.
  L=F, M=T, S=U: M would not say “T” (as M=T and L=F). Impossible.
  L=U, M=F, S=T: M would say “T” (as M=F and L=U), and S would say “not F” (as S=T and L=U). Possible.
  L=U, M=T, S=F: M would not say “T” (as M=T and L=U). Impossible.
  L=T, M=F, S=U: M would not say “T” (as M=F and L=T). Impossible.
  L=T, M=U, S=F: S would not say “not F” (as S=F and L=T). Impossible.

  So there is only one possible situation, and so the Professor can determine that: L=U=1965 (and also: M=F=1960, S=T=1969).

  Asking the question to M and S is the only situation where a single largest computer is identified, so this is the only solution.

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