S2T2

Jim Randell 9:58 am on 13 October 2020 Permalink Reply
Tags: by: Victor Bryant ( 108 )   

• 

  Jim Randell 9:58 am on 13 October 2020 Permalink | Reply

  See also: Teaser 2944.

  This Python program runs in 44ms.

  Run: [ @repl.it ]

  from enigma import subsets, printf
  
  # the names
  girls = "ADGK"
  boys = "BEHL"
  rabbits = "CFJM"
  
  # choose an ordering where exactly k of the original ordering is correct
  def choose(xs, k=1):
    for ys in subsets(xs, size=len, select="P"):
      if sum(x == y for (x, y) in zip(xs, ys)) == k:
        yield ys
  
  # choose an ordering for the boys
  for boy in choose(boys):
    # "neither H nor B live at number 3 [= index 2]"
    if boy[2] == 'H' or boy[2] == 'B': continue
  
    # choose an ordering for the rabbits
    for rabbit in choose(rabbits):
      # "J does not live at number 1 [=index 0]"
      if rabbit[0] == 'J': continue
      # "B's number is one less than C's"
      if boy.index('B') + 1 != rabbit.index('C'): continue
  
      # choose an ordering for the girls
      for girl in choose(girls):
        # "D does not live at number 1 [= index 0]"
        if girl[0] == 'D': continue
        # "G's number is one less than M's"
        if girl.index('G') + 1 != rabbit.index('M'): continue
  
        # output solution
        for (n, (g, b, r)) in enumerate(zip(girl, boy, rabbit), start=1):
          printf("{n}: {g} {b} {r}")
        printf()
  

  Solution: The occupants of each house are:

  1: Kelly, Harry, Flopsy
  2: Alice, Brian, Jumper
  3: Gail, Eric, Cottontail
  4: Donna, Laurie, Mopsy

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• 

  Frits 4:56 pm on 13 October 2020 Permalink | Reply

  from enigma import SubstitutedExpression
  
  girls   = ("", "Alice", "Donna", "Gail", "Kelly")
  boys    = ("", "Brian", "Eric", "Harry", "Laurie")
  rabbits = ("", "Cottontail", "Flopsy", "Jumper", "Mopsy")
  
  # the alphametic puzzle
  p = SubstitutedExpression(
    [
     # "B's number is one less than C's"
     "B + 1 = C",
     # "G's number is one less than M's" 
     "G + 1 = M",
     # listing gave exactly one girl, one boy and one rabbit at
     # her, his or its correct address
     "sum((A == 1, D == 2, G == 3, K == 4)) == 1",
     "sum((B == 1, E == 2, H == 3, L == 4)) == 1",
     "sum((C == 1, F == 2, J == 3, M == 4)) == 1",
    ],
    answer="ADGK, BEHL, CFJM",   
    digits=range(1,5),
    distinct=('ADGK', 'BEHL', 'CFJM'),
    # "D does not live at number 1"
    # "J does not live at number 1"
    # "neither H nor B live at number 3"
    d2i={1 : "CMDJ", 3 : "BH", 4 : "BG"}, 
    verbose=0,
    #reorder=0,
  )
  
  # Print answers
  for (_, ans) in p.solve(): 
    for k in "1234":
      x = [j+1 for x in ans for j, y in enumerate(str(x)) if y == k]
      print(f"house {k}: {girls[x[0]]:<6} {boys[x[1]]:<7} {rabbits[x[2]]}")
    
  # house 1: Kelly  Harry   Flopsy
  # house 2: Alice  Brian   Jumper
  # house 3: Gail   Eric    Cottontail
  # house 4: Donna  Laurie  Mopsy
  

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• 

  John Crabtree 6:34 pm on 13 October 2020 Permalink | Reply

  Flopsy must be at #1.
  Brian cannot be at #2, otherwise Jumper and Mopsy are both correct or both incorrect.
  And so Brian is at #1, Cottontail at #3, Jumper at #1, Mopsy at #4, and Gail at #3, etc

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