S2T2

Jim Randell 9:34 am on 14 February 2025 Permalink Reply
Tags: by: Victor Bryant ( 139 )   

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  Jim Randell 9:34 am on 14 February 2025 Permalink | Reply

  This Python program considers all possible recipients of the cards, and then eliminates candidates where the given conditions are not met. (A simple performance improvement would be to remove recipient candidates that do not include people we know received a card (i.e. C, E, G)).

  It runs in 166ms. (Internal runtime is 85ms).

  from enigma import (subsets, cproduct, multiset, map2str, printf)
  
  # multiple lookups on dict <d>
  def nget(d, k, n):
    while n > 0:
      k = d[k]
      n -= 1
    return k
  
  # labels for the girls and boys
  (gs, bs) = (tuple("ABCD"), tuple("EFGH"))
  
  # choose targets for the girls and boys
  for (tgs, tbs) in cproduct(subsets(xs, size=len, select='M') for xs in (bs, gs)):
    # combine them into a single map
    v = dict(zip(gs, tgs))
    v.update(zip(bs, tbs))
  
    # check the conditions:
    # "A's Valentine's Valentine's Valentine was E"
    if not (nget(v, 'A', 3) == 'E'): continue
  
    # "B's Valentine's Valentine's Valentine's Valentine was C"
    if not (nget(v, 'B', 4) == 'C'): continue
  
    # "F's Valentine's Valentine's Valentine's Valentine's Valentine's Valentine was G"
    if not (nget(v, 'F', 6) == 'G'): continue
  
    # count the targets of the cards
    m = multiset.from_seq(tgs, tbs)
  
    # only C, E, H received at least as many cards as their Valentines did
    if not all((m.count(x) >= m.count(v[x])) == (x in "CEH") for x in gs + bs): continue
  
    # output solution
    printf("{v}", v=map2str(v, arr="->", sep=" ", enc=""))
  

  Solution: Ann, Beth, Cleo, Di sent their cards to Huw, Ed, Guy, Ed.

  The full list is:

  A → H
  B → E
  C → G
  D → E
  E → C
  F → B or D
  G → C
  H → D or B

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