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Jim Randell 9:45 am on 30 May 2019 Permalink Reply
Tags: by: W Blackman ( 3 )   

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  Jim Randell 9:46 am on 30 May 2019 Permalink | Reply

  There are quite a few conditions. I started with the two conditions that deal with reversing one of the house numbers to get another number. Together these conditions give us the house numbers for two of the names and three of the jobs, so we can work out what the majority parity of the numbers is and fill out the remaining numbers appropriately.

  This Python program runs in 96ms.

  from enigma import (irange, filter2, is_prime, nreverse, is_square, subsets, flatten, printf)
  
  # select the first x in xs that satisfies f
  def select(xs, f):
    for x in xs:
      if f(x):
        return x
  
  # possible house numbers
  numbers = set(irange(10, 99))
  
  # split them into even and odd numbers
  (even, odd) = map(set, filter2(lambda n: n % 2 == 0, numbers))
  
  # complete a set of 6 house numbers
  def complete(ns):
    # count the even and odd numbers
    r0 = len(even.intersection(ns))
    r1 = len(odd.intersection(ns))
    # find the majority parity
    m = -1
    if r0 > 1: m += 1
    if r1 > 1: m += 2
    if m not in (0, 1): return
    # do we need to choose a minority number?
    for ys in subsets([odd, even][m].difference(ns), size=1 - [r1, r0][m]):
      # choose the remaining majority numbers
      for zs in subsets([even, odd][m].difference(ns), size=6 - len(ys) - len(ns)):
        s = ns.union(ys, zs)
        # sum the digits
        t = sum(flatten(divmod(n, 10) for n in s))
        # is a perfect square, and one of the numbers itself
        if not (t in s and is_square(t)): continue
        # return the candidate set
        yield (sorted(s), m, t)
  
  # consider Green's house number
  for Gre in numbers:
    # the reverse gives the number of the Architect's house
    Arc = nreverse(Gre)
    if Arc not in numbers: continue
    # and the difference between the squares
    # is the square of the number of the Journalist's house
    Jou = is_square(abs(Gre ** 2 - Arc ** 2))
    if Jou is None or Jou not in numbers: continue
  
    # Robinson's house number is a prime
    for Rob in numbers:
      if not is_prime(Rob): continue
      # and is the reverse of the Doctor's number
      Doc = nreverse(Rob)
      # which is also prime
      if not is_prime(Doc): continue
  
      # complete the set of numbers
      for (ns, m, t) in complete(set((Gre, Rob, Arc, Jou, Doc))):
        # the sum of the digits is the number of the Solicitor's house
        Sol = t
        # Black is in the minority parity house
        Bla = select(ns, (lambda n: n % 2 != m))
  
        # (at least) one of the houses next to Robinson is vacant
        vacant = set([Rob - 2, Rob + 2]).difference(ns)
        if len(vacant) < 1: continue
  
        # the extreme numbers are occupied by Jones and the Dentist
        for (Jon, Den) in subsets([ns[0], ns[-1]], size=2, permute=1):
  
          # and we now have 5 of the 6 professions
          ps = set([Arc, Jou, Doc, Sol, Den])
          if len(ps) != 5: continue
          Sto = select(ns, (lambda n: n not in ps))
  
          # and 4 of the 6 names
          ss = set([Gre, Rob, Bla, Jon])
          if len(ss) != 4: continue
          for (Smi, Whi) in subsets(ss.symmetric_difference(ns), size=2, permute=1):
  
            # Smith and the Stockbroker live next door to each other
            if not (abs(Smi - Sto) == 2): continue
  
            # output solutions
            name = { Gre: 'Green', Rob: 'Robinson', Bla: 'Black', Jon: 'Jones', Smi: 'Smith', Whi: 'White' }
            job = { Arc: 'Architect', Jou: 'Journalist', Doc: 'Doctor', Sol: 'Solicitor', Den: 'Dentist', Sto: 'Stockbroker' }
            for n in ns:
              printf("{n}: {name} ({job})", name=name[n], job=job[n])
            printf("vacant = {vacant}", vacant=sorted(vacant))
            printf()
  

  Solution: The vacant house is number 29. White is the Solicitor. Robinson is the Stockbroker.

  The solution is completely determined:

  13: Jones (Doctor)
  31: Robinson (Stockbroker)
  33: Smith (Journalist)
  49: White (Solicitor)
  56: Black (Architect)
  65: Green (Dentist)

  29: vacant

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