Sunday Times Teaser 3093 – Shout Snap!

by BRG on January 1, 2022

by Victor Bryant

Published Sunday January 02 2022 (link)

My grandson and I play a simple card game. We have a set of fifteen cards on each of which is one of the words ACE, TWO, THREE, FOUR, FIVE, SIX, SEVEN, EIGHT, NINE, TEN, JACK, QUEEN, KING, SHOUT and SNAP. We shuffle the cards and then display them one at a time. Whenever two consecutive cards have a letter of the alphabet occurring on both we race to shout “Snap!”. In a recent game there were no snaps. I counted the numbers of cards between the “picture-cards” (J/Q/K) and there was the same number between the first and second picture-cards occurring as between the second and third. Also, the odd-numbered cards (3 to 9) appeared in increasing order during the game.

In order, what were the first six cards?

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Brian Gladman permalink

In my first effort, I added the constraints on the four odd numbers and the court card positions outside the sequence generator but this turned out to be very slow so I had to add the constraints inside the generator to obtain a reasonable performance. Also ‘NigelR’ noticed here that cards containing ‘E’s must be at even positions and this provides a further major performance improvement.


from itertools import combinations

# all fifteen cards (since there are eight cards with 'E's and seven
# without, the 'E' cards must be in even positions to avoid snaps)
wrds = ('ACE', 'TWO',  'THREE', 'FOUR', 'FIVE', 'SIX', 'SEVEN', 'EIGHT', 
       'NINE', 'TEN', 'JACK', 'QUEEN', 'KING',  'SHOUT', 'SNAP')

# the four odd cards that occur in order
odds = ('THREE', 'FIVE', 'SEVEN', 'NINE')

# the three court cards
ccrd =  {'JACK', 'QUEEN', 'KING'}

# record all card pairs that can be adjacent
ok = set()
for a, b in combinations(wrds, 2):
  if not set(a).intersection(b):
    ok.update([(a, b), (b, a)])

# generate card sequences without snaps, with
# court cards equally spaced and the designated 
# odd cards apppearing in order
def ns_seq(cards, ix_cc=(), nodd=0, seq=()):
  if not cards:
      yield seq
  else:
    pos_even = not (len(seq) & 1)
    # try to add another card to the sequence
    for i, c in enumerate(cards):
      if not seq or (c, seq[-1]) in ok:
        
        # ensure all 'E' cards are in even positions
        if pos_even and 'E' not in c:
          continue
        
        # ensure the equal spacing of the Jack, Queen and King
        nix_cc = ix_cc
        if c in ccrd:
          nix_cc += (len(seq),)
          # if we have seen all of them, check for equal spacing 
          if len(nix_cc) == 3 and nix_cc[0] + nix_cc[2] != 2 * nix_cc[1]:
            continue    
        
        # ensure that THREE, FIVE, SEVEN and NINE are seen in order
        if c in odds and odds.index(c) != nodd:
          continue
        
        # add further cards
        yield from ns_seq(cards[:i] + cards[i + 1:], 
                          nix_cc, nodd + (c in odds), seq + (c,))

sol = set()                      
for s in ns_seq(wrds):
  print(f"{' '.join(s[:6])} [{' '.join(s[6:])}]")

from itertools import combinations

# all fifteen cards (since there are eight cards with 'E's and seven

# without, the 'E' cards must be in even positions to avoid snaps)

wrds = ('ACE', 'TWO', 'THREE', 'FOUR', 'FIVE', 'SIX', 'SEVEN', 'EIGHT',

'NINE', 'TEN', 'JACK', 'QUEEN', 'KING', 'SHOUT', 'SNAP')

# the four odd cards that occur in order

odds = ('THREE', 'FIVE', 'SEVEN', 'NINE')

# the three court cards

ccrd = {'JACK', 'QUEEN', 'KING'}

# record all card pairs that can be adjacent

ok = set()

for a, b in combinations(wrds, 2):

if not set(a).intersection(b):

ok.update([(a, b), (b, a)])

# generate card sequences without snaps, with

# court cards equally spaced and the designated

# odd cards apppearing in order

def ns_seq(cards, ix_cc=(), nodd=0, seq=()):

if not cards:

yield seq

else:

pos_even = not (len(seq) & 1)

# try to add another card to the sequence

for i, c in enumerate(cards):

if not seq or (c, seq[-1]) in ok:

# ensure all 'E' cards are in even positions

if pos_even and 'E' not in c:

continue

# ensure the equal spacing of the Jack, Queen and King

nix_cc = ix_cc

if c in ccrd:

nix_cc += (len(seq),)

# if we have seen all of them, check for equal spacing

if len(nix_cc) == 3 and nix_cc[0] + nix_cc[2] != 2 * nix_cc[1]:

continue

# ensure that THREE, FIVE, SEVEN and NINE are seen in order

if c in odds and odds.index(c) != nodd:

continue

# add further cards

yield from ns_seq(cards[:i] + cards[i + 1:],

nix_cc, nodd + (c in odds), seq + (c,))

sol = set()

for s in ns_seq(wrds):

print(f"{' '.join(s[:6])} [{' '.join(s[6:])}]")

Sunday Times Teaser 3093 – Shout Snap!

by Victor Bryant

Published Sunday January 02 2022 (link)

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