S2T2

Jim Randell 2:31 pm on 26 November 2019 Permalink Reply
Tags: by: R Postill ( 20 )   

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  Jim Randell 2:32 pm on 26 November 2019 Permalink | Reply

  This Python program runs in 73ms.

  from enigma import (defaultdict, irange, is_prime, nreverse, digrt, subsets, update, printf)
  
  # collect <answers> -> <ages>
  d = defaultdict(list)
  
  # consider possible ages
  for n in irange(25, 80):
    # the statements
    ss = (
      # 1. "Age is under 55?"
      (n < 55),
      # 2. "Age is prime?"
      is_prime(n),
      # 3. "Reverse of age is prime?"
      is_prime(nreverse(n)),
      # 4. "Digital root of age is even?"
      (digrt(n) % 2 == 0),
    )
    d[ss].append(n)
  
  # generate sequences with two (different) values swapped
  def swap(s):
    s = list(s)
    # swap two of the values
    for ((i, x), (j, y)) in subsets(enumerate(s), size=2):
      if x != y: yield tuple(update(s, [(i, y), (j, x)]))
  
  # find values for the first three questions where the final question gives a definite answer
  Bool = (True, False)
  for k in subsets(Bool, size=3, select="M"):
    # possible mistaken keys
    ks = list(k + (x,) for x in Bool)
    # each must lead to a single answer
    if not all(len(d[k]) == 1 for k in ks): continue
    # consider possible mistaken keys
    for k in ks:
      m = d[k][0] # mistaken age
      # look for possible real keys
      for r in swap(k):
        # possible real age
        for n in d[r]:
          # must be more than 20 years difference
          if abs(n - m) > 20:
            printf("age = {n}, real = {r}; swap = {k}, age = {m}")
  

  Solution: The setter’s age is 71.

  ---

  There is only one set of values for the answers to the first three questions that lead to two ages that can be differentiated by the answer to the fourth question.

  If all the first three questions are answered “Yes”, then:

  If the answer to the fourth question is “Yes”, the age is 31.
  If the answer to the fourth question is “No”, the age is 37.

  The setter then discovers that he has exchanged the places of two of the answers.

  So the answer sent cannot be: (“Yes”, “Yes”, “Yes”, “Yes”), as swapping any two of them would make no difference.

  So the sent answers must have been: (“Yes”, “Yes”, “Yes”, “No”). Leading the puzzler to believe that the setters age was 37.

  But this is incorrect “by well over 20 years”, so the setter must be much less than 17 (not possible) or much more than 57.

  If we move the “No” into different positions we get:

  (“No”, “Yes”, “Yes”, “Yes”) → 71
  (“Yes”, “No”, “Yes”, “Yes”) → 35, 38
  (“Yes”, “Yes”, “No”, “Yes”) → 29, 47, 53

  Only the first of these gives an age much more than 57, so the answers for the first and fourth question were accidentally swapped.

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