S2T2

Jim Randell 12:12 pm on 2 April 2020 Permalink Reply
Tags: by: Dr V W Bryant ( 5 )   

• 

  Jim Randell 12:12 pm on 2 April 2020 Permalink | Reply

  In order to get a unique solution I had to add a couple of extra “implied” conditions (the kind that got me into trouble in Enigma 99).

  So: “… is going to promote Chamberton to Minister of the Mails, or above”, implies that C’s current position is below MoM.

  and: “Disreel will become Deputy Premier only if …”, implies that D is not currently Deputy Premier. (Also the fact that A would serve under D as Deputy Premier implies that D does not currently hold this position).

  and (maybe): “… Attler has made it clear that if he is going to be junior to Chamberton …”, implies that A is not currently junior to C (although this extra condition is not required to get a unique solution).

  With these conditions made explicit we find there is a single answer to the puzzle.

  This Python program runs in 86ms.

  Run: [ @repl.it ]

  from enigma import (defaultdict, irange, subsets, printf)
  
  # "p -> q" = "if p then q", "q if p", "p only if q"
  implies = lambda p, q: not(p) or q
  
  # record (by number of demotions) who occupies position 4
  r = defaultdict(set)
  
  # consider "before" positions
  for before in subsets(irange(1, 5), size=5, select="P"):
    (bA, bB, bC, bD, bE) = before
  
    # [implied] D is not currently 1
    if bD == 1: continue
  
    # [implied] A is not currently junior to C
    if (bC < bA): continue
  
    # [implied] C is currently below 3
    if not (bC > 3): continue
  
    # consider "after positions"
    for after in subsets(irange(1, 5), size=5, select="P"):
      (aA, aB, aC, aD, aE) = after
  
      # nobody keeps the same post
      if any(bX == aX for (bX, aX) in zip(before, after)): continue
  
      # if A is junior to C, then D must be 1
      if not implies(aA > aC, aD == 1): continue
  
      # D becomes 1 only if B becomes 3
      if not implies(aD == 1, aB == 3): continue
  
      # C is to be promoted to 3 or above
      if not (aC < 4 and aC < bC): continue
  
      # E is to be promoted
      if not (aE < bE): continue
  
      # B is to be demoted ...
      if not (aB > bB): continue
  
      # ... but will become senior to someone who was his junior
      if not any(aB < aX and bB > bX for (bX, aX) in zip(before, after)): continue
  
      # count the number of demotions
      d = sum(aX > bX for (bX, aX) in zip(before, after))
  
      printf("[d={d}, A: {bA}->{aA}; B: {bB}->{aB}; C: {bC}->{aC}; D: {bD}->{aD}; E: {bE}->{aE}]")
      b = dict(zip(before, "ABCDE"))
      a = dict(zip(after, "ABCDE"))
      r[d].add((b[4], a[4]))
  
  # look for the fewest number of demotions
  k = min(r.keys())
  for (b4, a4) in r[k]:
    printf("{k} demotions: SoS = {b4}->{a4}")
  

  Solution: Chamberton is the current Secretary of Science. Edane will be the new Secretary of Science.

  There is only one scenario that has only 2 demotions:

  A: demoted from Deputy Premier to Head Whip
  B: demoted from Chancellor to Minister of Mails
  C: promoted from Secretary of Science to Chancellor
  D: promoted from Minster of Mails to Deputy Premier
  E: promoted from Head Whip to Secretary of Science

  We are told B is to be demoted, and someone else who was above B must also be demoted under B, so we cannot do better than 2 demotions.

  There are 2 further scenarios that satisfy the conditions that have 3 demotions.

  LikeLike

• 

  John Crabtree 10:06 pm on 3 April 2020 Permalink | Reply

  Let the five positions in order of rank be P1, P2, P3, P4 and P5.

  C and E will be promoted, D can be promoted, and B has somebody senior to him, and so A is currently in P1.
  B can be demoted to P3, and so is currently in P2.
  A will move to P4 or P5 (lower than B), and so will be junior to C (P3 or above), and so D moves to P1, and so B moves to P3, and so C moves to P2.
  To minimise the number of demotions A moves to P5, and E moves from P5 to P4.
  The current positions are not in order, and so currently C is in P4, and D is in P3.

  Chamberton is the current Secretary of Science.
  Edane will become the Secretary of Science.

  LikeLike