Sunday Times Teaser 2903 – What’s My Card

by John Owen

Published May 13 2018 (link)

Four expert logicians play a game with a pack of six cards, numbered from 1 to 6. The cards are shuffled and each draws a card, holding it in front of him so that he cannot see his own number but can see the numbers held by the others. The winner is the player who can first deduce what number he is holding.

Each player in turn is asked to announce the sum of two numbers that he can see on the other cards. One game started with Alf announcing 6. After a long pause, no-one claimed victory, so Bert then announced 5. There was a significant pause, but before Charlie spoke, someone claimed victory.

Which cards did Alf and Bert hold, and which cards remained on the table?

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Brian Gladman permalink

Here is my code for this teaser. I was only able to get this code working after stumbling on Jim Randell’s solution on repl.it which you can see here. This allowed me to correct the two marked sections on which I had previously made little progress. To run this code you will also need the code on this page which is also based on Jim’s work (you need to put this in the same directory as this code).


from itertools import permutations
from partition_unique import partition_unique

# the player's labels and the cards
A, B, C, D = players = range(4)
cards = range(1, 7)

# given the 4-tuple of cards held by A, B, C and D, return the
# card held by player P 
def card(P):
  return lambda t: t[P]

# given the 4-tuple of cards held by A, B, C and D, return the
# 3-tuple of cards seen by player P 
def seen(P):
  return lambda t: tuple(x for x in t if x != t[P])

# find the set of all possible four card arrangements for (A, B, C, D)
ca_abcd = set(permutations(cards, 4))

# find the set of arrangements for which A can declare a sum of six
ca_abcd = set(x for x in ca_abcd if 6 in (x[B] + x[C], x[B] + x[D], x[C] + x[D]))

# remove arrangements for which any player can announce their number at this point
t = set()
for P in players:
  t.update(partition_unique(ca_abcd, seen(P), card(P))[0])
ca_abcd.difference_update(t)

# find the set of arrangements for which B can declare a sum of five
ca_abcd = set(x for x in ca_abcd if 5 in (x[A] + x[C], x[A] + x[D], x[C] + x[D]))

# remove arrangements for which any player can announce their number at this point
t = set()
for P in players:
  t.update(partition_unique(ca_abcd, seen(P), card(P))[0])
ca_abcd.difference_update(t)

# output arrangements that remain unresolved
for s in ca_abcd:
  t = set(cards).difference(s)
  print(f'(A, B) = ({s[A]}, {s[B]}), (C, D) = ({s[C]}, {s[D]}), table = {t}')

from itertools import permutations

from partition_unique import partition_unique

# the player's labels and the cards

A, B, C, D = players = range(4)

cards = range(1, 7)

# given the 4-tuple of cards held by A, B, C and D, return the

# card held by player P

def card(P):

return lambda t: t[P]

# given the 4-tuple of cards held by A, B, C and D, return the

# 3-tuple of cards seen by player P

def seen(P):

return lambda t: tuple(x for x in t if x != t[P])

# find the set of all possible four card arrangements for (A, B, C, D)

ca_abcd = set(permutations(cards, 4))

# find the set of arrangements for which A can declare a sum of six

ca_abcd = set(x for x in ca_abcd if 6 in (x[B] + x[C], x[B] + x[D], x[C] + x[D]))

# remove arrangements for which any player can announce their number at this point

t = set()

for P in players:

t.update(partition_unique(ca_abcd, seen(P), card(P))[0])

ca_abcd.difference_update(t)

# find the set of arrangements for which B can declare a sum of five

ca_abcd = set(x for x in ca_abcd if 5 in (x[A] + x[C], x[A] + x[D], x[C] + x[D]))

# remove arrangements for which any player can announce their number at this point

t = set()

for P in players:

t.update(partition_unique(ca_abcd, seen(P), card(P))[0])

ca_abcd.difference_update(t)

# output arrangements that remain unresolved

for s in ca_abcd:

t = set(cards).difference(s)

print(f'(A, B) = ({s[A]}, {s[B]}), (C, D) = ({s[C]}, {s[D]}), table = {t}')

Sunday Times Teaser 2903 – What’s My Card

by John Owen

Published May 13 2018 (link)

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