When is Cheryl’s birthday?

推理

第一句话确定：July 14 July 16 August 14 August 15 August 17(告诉B日期不可能为18，19，==>告诉A的月份不可能为May，June)
第二句话确定：July 16 August 15 August 17(日期14有两个，B不可能确定，排除）
第三句话确定：July 16（月份August有两个，A不能确定，推出July16)

###Khanacademy

Python

#!/usr/bin/env python
# -*- coding: utf-8 -*-

DATES = ['May 15',    'May 16',    'May 19',
        'June 17',   'June 18',
        'July 14',   'July 16',
      'August 14', 'August 15', 'August 17']

def Month(date): return date.split()[0]
def Day(date):   return date.split()[1]

#print Month('May 15')
#out:May
#print Day('May 15')
#out:15

def tell(part, possible_dates=DATES):
    "Cheryl tells a part of her birthdate to someone; return a new list of possible dates that match the part."
    return [date for date in possible_dates if part in date]

def know(possible_dates):
    "A person knows the birthdate if they have exactly one possible date."
    return len(possible_dates) == 1

#print tell('May')
#out:['May 15', 'May 16', 'May 19']
#print tell('15')
#out:['May 15', 'August 15']
#print know(tell('15'))
#out:False

def cheryls_birthday(possible_dates=DATES):
    "Return a list of the possible dates for which statements 3 to 5 are true."
    return filter(statements3to5, possible_dates)

def statements3to5(date): return statement3(date) and statement4(date) and statement5(date)

## TO DO: define statement3, statement4, statement5

def statement3(date):
    "Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too."
    possible_dates = tell(Month(date))
    return (not know(possible_dates)
            and all(not know(tell(Day(d)))
                    for d in possible_dates))

#print statement3('May 15')
#out:False
#print filter(statement3,DATES)
#out:['July 14', 'July 16', 'August 14', 'August 15', 'August 17']

def statement4(date):
    "Bernard: At first I don't know when Cheryl's birthday is, but I know now."
    at_first = tell(Day(date))
    return (not know(at_first)
            and know(filter(statement3, at_first)))

#print filter(statement4,filter(statement3,DATES))
#out:['July 16', 'August 15', 'August 17']

def statement5(date):
    "Albert: Then I also know when Cheryl's birthday is."
    return know(filter(statement4, tell(Month(date))))

print cheryls_birthday()
#out:['July 16']
print know(cheryls_birthday())
#out:True

Mathematica(1)

(*
Procedural answer to the question posted here:
"http://nbviewer.ipython.org/url/norvig.com/ipython/Cheryl.ipynb"

Doing this in other fun mathematica ways is left as an exercise for the reader :)
*)

In[665]:= str  = "    May 15     May 16     May 19
     June 17    June 18
     July 14    July 16
   August 14  August 15  August 17" ;

dates = Partition[StringSplit[str], 2]

Out[666]= {{"May", "15"}, {"May", "16"}, {"May", "19"}, {"June",
  "17"}, {"June", "18"}, {"July", "14"}, {"July", "16"}, {"August",
  "14"}, {"August", "15"}, {"August", "17"}}

(* 3. albert didn't know when cheryl's birthday was, but
knew bernard didn't know either. he has revealed that he's holding a
month that does not permit bernard to immediately know. bernard would
only immediately know if the day was unique in the list *)

In[667]:=

monthsWithUniqueDay =
 GatherBy[dates, Last] // Select[Length[#] == 1 &] // Catenate //
  Map[First]

Out[667]= {"May", "June"}

(* 4. bernard reveals his initial day was ambiguous, it
mapped to multiple months *)

In[668]:=

ambiguousDays =
  GatherBy[dates, Last] // Select[Length[#] > 1 &] // Catenate //
    Map[Last] // Union;

bernardInitial = dates // Select[MemberQ[ambiguousDays, Last[#] ] &]

Out[669]= {{"May", "15"}, {"May", "16"}, {"June", "17"}, {"July",
  "14"}, {"July", "16"}, {"August", "14"}, {"August",
  "15"}, {"August", "17"}}

(* 4.3 bernard has incorporated albert's information,
ruling out any months with unique days *)

In[670]:=

bernardNoUniqueDays =
 bernardInitial // Select[! MemberQ[monthsWithUniqueDay, First[#]] &]

Out[670]= {{"July", "14"}, {"July", "16"}, {"August",
  "14"}, {"August", "15"}, {"August", "17"}}

(* 4.6 bernard says this is good enough to give him the
answer. so what days are potentially unambiguous for him, that are
unique day numbers in the set? *)

In[671]:=

bernardCandidateDays =
 Tally[bernardNoUniqueDays[[All, 2]]] // Select[Last[#] == 1 &] //
  Map[First]

Out[671]= {"16", "15", "17"}

(* since these are the unique day numbers bernard has, we
know the final answer must be one of these month/day combinations *)

In[672]:=

bernardCandidateAnswers =
 Select[bernardNoUniqueDays, MemberQ[bernardCandidateDays, Last@#] &]

Out[672]= {{"July", "16"}, {"August", "15"}, {"August", "17"}}

(* 5. albert says this is good enough to give *him* the answer. which
means albert sees here an unambiguous month. What month is
unambiguous in this set? because that's our answer *)

Select[
 GatherBy[bernardCandidateAnswers, First], Length[#] == 1 &]

Out[673]= {{{"July", "16"}}}

Mathematica(2)

cand = {{"May", 15}, {"May", 16}, {"May", 19}, {"June", 17}, {"June",
    18}, {"July", 14}, {"July", 16}, {"August", 14}, {"August",
    15}, {"August", 17}};
c1[n_] :=
 With[{rem = Cases[Tally[n[[All, 2]]], {x_, _?(# == 1 &)} :> x]},
  DeleteCases[
   n, {Alternatives @@ (Cases[n, {_, Alternatives @@ rem}][[All,
        1]]), _}]]
c2[n_] :=
 With[{rem = Cases[Tally[n[[All, 2]]], {x_, _?(# == 1 &)} :> x]},
  Cases[n, {_, Alternatives @@ rem}]]
c3[n_] :=
 With[{rem = Cases[Tally[n[[All, 1]]], {x_, _?(# == 1 &)} :> x]},
  Cases[n, {Alternatives @@ rem, _}]]
Composition[
  Row[{"Cheryl's Birthday is "}~Join~#, Spacer[2]] &, #[[1]] &, c3, c2,
   c1][cand]

cand is candidate birthdays
c1 to c3 are the clues from the three statements:(i) rule out months that have unique day (ii) rule out birthdays without unique days (iii) find remaining birthday which has unique month the rest is for “prettiness”

参考

• python 代码
• Khanacademy
• Mathematica