Cheryl's birthday

Cheryl's birthday is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is.

Cheryl gave them a list of 10 possible dates:

May 15, May 16, May 19 June 17, June 18 July 14, July 16 August 14, August 15, August 17

Cheryl then tells Albert and Bernard separately the month and the day of the birthday respectively.

1) Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.

2) Bernard: At first I don't know when Cheryl's birthday is, but I know now.

3) Albert: Then I also know when Cheryl's birthday is.

Task

Write a program in your language to deduce, by successive elimination, Cheryl's birthday.

See the Wikipedia article of the same name.

Related task

• Sum and Product Puzzle

AppleScript

<lang applescript>use AppleScript version "2.4" use framework "Foundation" use scripting additions

property M : 1 -- Month property D : 2 -- Day

on run

   -- The MONTH with only one remaining day
   -- among the DAYs with unique months,
   -- EXCLUDING months with unique days,
   -- in Cheryl's list:
   
   showList(uniquePairing(M, ¬
       uniquePairing(D, ¬
           monthsWithUniqueDays(false, ¬
               map(composeList({tupleFromList, |words|, toLower}), ¬
                   splitOn(", ", ¬
                       "May 15, May 16, May 19, June 17, June 18, " & ¬
                       "July 14, July 16, Aug 14, Aug 15, Aug 17"))))))
   
   --> "[('july', '16')]"

end run

-- QUERY FUNCTIONS ----------------------------------------

-- monthsWithUniqueDays :: Bool -> [(Month, Day)] -> [(Month, Day)] on monthsWithUniqueDays(blnInclude, xs)

   set _months to map(my fst, uniquePairing(D, xs))
   script uniqueDay
       on |λ|(md)
           set bln to elem(fst(md), _months)
           if blnInclude then
               bln
           else
               not bln
           end if
       end |λ|
   end script
   filter(uniqueDay, xs)

end monthsWithUniqueDays

-- uniquePairing :: DatePart -> [(M, D)] -> [(M, D)] on uniquePairing(dp, xs)

   script go
       property f : my mReturn(item dp of {my fst, my snd})
       on |λ|(md)
           set dct to f's |λ|(md)
           script unique
               on |λ|(k)
                   set mb to lookupDict(k, dct)
                   if Nothing of mb then
                       false
                   else
                       1 = length of (Just of mb)
                   end if
               end |λ|
           end script
           set uniques to filter(unique, keys(dct))
           script found
               on |λ|(tpl)
                   elem(f's |λ|(tpl), uniques)
               end |λ|
           end script
           filter(found, xs)
       end |λ|
   end script
   bindPairs(xs, go)

end uniquePairing

-- bindPairs :: [(M, D)] -> ((Dict Text [Text], Dict Text [Text]) -- -> [(M, D)]) -> [(M, D)] on bindPairs(xs, f)

   tell mReturn(f)
       |λ|(Tuple(dictFromPairs(xs), ¬
           dictFromPairs(map(my swap, xs))))
   end tell

end bindPairs

-- dictFromPairs :: [(M, D)] -> Dict Text [Text] on dictFromPairs(mds)

   set gps to groupBy(|on|(my eq, my fst), ¬
       sortBy(comparing(my fst), mds))
   script kv
       on |λ|(gp)
           Tuple(fst(item 1 of gp), map(my snd, gp))
       end |λ|
   end script
   mapFromList(map(kv, gps))

end dictFromPairs

-- LIBRARY GENERICS ---------------------------------------

-- comparing :: (a -> b) -> (a -> a -> Ordering) on comparing(f)

   script
       on |λ|(a, b)
           tell mReturn(f)
               set fa to |λ|(a)
               set fb to |λ|(b)
               if fa < fb then
                   -1
               else if fa > fb then
                   1
               else
                   0
               end if
           end tell
       end |λ|
   end script

end comparing

-- compose (<<<) :: (b -> c) -> (a -> b) -> a -> c on compose(f, g)

   script
       property mf : mReturn(f)
       property mg : mReturn(g)
       on |λ|(x)
           mf's |λ|(mg's |λ|(x))
       end |λ|
   end script

end compose

-- composeList :: [(a -> a)] -> (a -> a) on composeList(fs)

   script
       on |λ|(x)
           script
               on |λ|(f, a)
                   mReturn(f)'s |λ|(a)
               end |λ|
           end script
           
           foldr(result, x, fs)
       end |λ|
   end script

end composeList

-- drop :: Int -> [a] -> [a] -- drop :: Int -> String -> String on drop(n, xs)

   set c to class of xs
   if c is not script then
       if c is not string then
           if n < length of xs then
               items (1 + n) thru -1 of xs
           else
               {}
           end if
       else
           if n < length of xs then
               text (1 + n) thru -1 of xs
           else
               ""
           end if
       end if
   else
       take(n, xs) -- consumed
       return xs
   end if

end drop

-- dropAround :: (a -> Bool) -> [a] -> [a] -- dropAround :: (Char -> Bool) -> String -> String on dropAround(p, xs)

   dropWhile(p, dropWhileEnd(p, xs))

end dropAround

-- dropWhile :: (a -> Bool) -> [a] -> [a] -- dropWhile :: (Char -> Bool) -> String -> String on dropWhile(p, xs)

   set lng to length of xs
   set i to 1
   tell mReturn(p)
       repeat while i ≤ lng and |λ|(item i of xs)
           set i to i + 1
       end repeat
   end tell
   drop(i - 1, xs)

end dropWhile

-- dropWhileEnd :: (a -> Bool) -> [a] -> [a] -- dropWhileEnd :: (Char -> Bool) -> String -> String on dropWhileEnd(p, xs)

   set i to length of xs
   tell mReturn(p)
       repeat while i > 0 and |λ|(item i of xs)
           set i to i - 1
       end repeat
   end tell
   take(i, xs)

end dropWhileEnd

-- elem :: Eq a => a -> [a] -> Bool on elem(x, xs)

   considering case
       xs contains x
   end considering

end elem

-- enumFromToInt :: Int -> Int -> [Int] on enumFromToInt(M, n)

   if M ≤ n then
       set lst to {}
       repeat with i from M to n
           set end of lst to i
       end repeat
       return lst
   else
       return {}
   end if

end enumFromToInt

-- eq (==) :: Eq a => a -> a -> Bool on eq(a, b)

   a = b

end eq

-- filter :: (a -> Bool) -> [a] -> [a] on filter(f, xs)

   tell mReturn(f)
       set lst to {}
       set lng to length of xs
       repeat with i from 1 to lng
           set v to item i of xs
           if |λ|(v, i, xs) then set end of lst to v
       end repeat
       return lst
   end tell

end filter

-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs)

   tell mReturn(f)
       set v to startValue
       set lng to length of xs
       repeat with i from 1 to lng
           set v to |λ|(v, item i of xs, i, xs)
       end repeat
       return v
   end tell

end foldl

-- foldr :: (a -> b -> b) -> b -> [a] -> b on foldr(f, startValue, xs)

   tell mReturn(f)
       set v to startValue
       set lng to length of xs
       repeat with i from lng to 1 by -1
           set v to |λ|(item i of xs, v, i, xs)
       end repeat
       return v
   end tell

end foldr

-- fst :: (a, b) -> a on fst(tpl)

   if class of tpl is record then
       |1| of tpl
   else
       item 1 of tpl
   end if

end fst

-- Typical usage: groupBy(on(eq, f), xs) -- groupBy :: (a -> a -> Bool) -> [a] -> a on groupBy(f, xs)

   set mf to mReturn(f)
   
   script enGroup
       on |λ|(a, x)
           if length of (active of a) > 0 then
               set h to item 1 of active of a
           else
               set h to missing value
           end if
           
           if h is not missing value and mf's |λ|(h, x) then
               {active:(active of a) & {x}, sofar:sofar of a}
           else
               {active:{x}, sofar:(sofar of a) & {active of a}}
           end if
       end |λ|
   end script
   
   if length of xs > 0 then
       set dct to foldl(enGroup, {active:{item 1 of xs}, sofar:{}}, rest of xs)
       if length of (active of dct) > 0 then
           sofar of dct & {active of dct}
       else
           sofar of dct
       end if
   else
       {}
   end if

end groupBy

-- insertMap :: Dict -> String -> a -> Dict on insertMap(rec, k, v)

   tell (current application's NSMutableDictionary's ¬
       dictionaryWithDictionary:rec)
       its setValue:v forKey:(k as string)
       return it as record
   end tell

end insertMap

-- intercalateS :: String -> [String] -> String on intercalateS(sep, xs)

   set {dlm, my text item delimiters} to {my text item delimiters, sep}
   set s to xs as text
   set my text item delimiters to dlm
   return s

end intercalateS

-- Just :: a -> Maybe a on Just(x)

   {type:"Maybe", Nothing:false, Just:x}

end Just

-- keys :: Dict -> [String] on keys(rec)

   (current application's NSDictionary's dictionaryWithDictionary:rec)'s allKeys() as list

end keys

-- lookupDict :: a -> Dict -> Maybe b on lookupDict(k, dct)

   set ca to current application
   set v to (ca's NSDictionary's dictionaryWithDictionary:dct)'s objectForKey:k
   if v ≠ missing value then
       Just(item 1 of ((ca's NSArray's arrayWithObject:v) as list))
   else
       Nothing()
   end if

end lookupDict

-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: First-class m => (a -> b) -> m (a -> b) on mReturn(f)

   if class of f is script then
       f
   else
       script
           property |λ| : f
       end script
   end if

end mReturn

-- map :: (a -> b) -> [a] -> [b] on map(f, xs)

   tell mReturn(f)
       set lng to length of xs
       set lst to {}
       repeat with i from 1 to lng
           set end of lst to |λ|(item i of xs, i, xs)
       end repeat
       return lst
   end tell

end map

-- mapFromList :: [(k, v)] -> Dict on mapFromList(kvs)

   set tpl to unzip(kvs)
   script
       on |λ|(x)
           x as string
       end |λ|
   end script
   (current application's NSDictionary's ¬
       dictionaryWithObjects:(|2| of tpl) ¬
           forKeys:map(result, |1| of tpl)) as record

end mapFromList

-- min :: Ord a => a -> a -> a on min(x, y)

   if y < x then
       y
   else
       x
   end if

end min

-- Nothing :: Maybe a on Nothing()

   {type:"Maybe", Nothing:true}

end Nothing

-- e.g. sortBy(|on|(compare, |length|), ["epsilon", "mu", "gamma", "beta"]) -- on :: (b -> b -> c) -> (a -> b) -> a -> a -> c on |on|(f, g)

   script
       on |λ|(a, b)
           tell mReturn(g) to set {va, vb} to {|λ|(a), |λ|(b)}
           tell mReturn(f) to |λ|(va, vb)
       end |λ|
   end script

end |on|

-- partition :: predicate -> List -> (Matches, nonMatches) -- partition :: (a -> Bool) -> [a] -> ([a], [a]) on partition(f, xs)

   tell mReturn(f)
       set ys to {}
       set zs to {}
       repeat with x in xs
           set v to contents of x
           if |λ|(v) then
               set end of ys to v
           else
               set end of zs to v
           end if
       end repeat
   end tell
   Tuple(ys, zs)

end partition

-- show :: a -> String on show(e)

   set c to class of e
   if c = list then
       showList(e)
   else if c = record then
       set mb to lookupDict("type", e)
       if Nothing of mb then
           showDict(e)
       else
           script
               on |λ|(t)
                   if "Either" = t then
                       set f to my showLR
                   else if "Maybe" = t then
                       set f to my showMaybe
                   else if "Ordering" = t then
                       set f to my showOrdering
                   else if "Ratio" = t then
                       set f to my showRatio
                   else if class of t is text and t begins with "Tuple" then
                       set f to my showTuple
                   else
                       set f to my showDict
                   end if
                   tell mReturn(f) to |λ|(e)
               end |λ|
           end script
           tell result to |λ|(Just of mb)
       end if
   else if c = date then
       "\"" & showDate(e) & "\""
   else if c = text then
       "'" & e & "'"
   else if (c = integer or c = real) then
       e as text
   else if c = class then
       "null"
   else
       try
           e as text
       on error
           ("«" & c as text) & "»"
       end try
   end if

end show

-- showList :: [a] -> String on showList(xs)

   "[" & intercalateS(", ", map(my show, xs)) & "]"

end showList

-- showTuple :: Tuple -> String on showTuple(tpl)

   set ca to current application
   script
       on |λ|(n)
           set v to (ca's NSDictionary's dictionaryWithDictionary:tpl)'s objectForKey:(n as string)
           if v ≠ missing value then
               unQuoted(show(item 1 of ((ca's NSArray's arrayWithObject:v) as list)))
           else
               missing value
           end if
       end |λ|
   end script
   "(" & intercalateS(", ", map(result, enumFromToInt(1, length of tpl))) & ")"

end showTuple

-- snd :: (a, b) -> b on snd(tpl)

   if class of tpl is record then
       |2| of tpl
   else
       item 2 of tpl
   end if

end snd

-- Enough for small scale sorts. -- Use instead sortOn :: Ord b => (a -> b) -> [a] -> [a] -- which is equivalent to the more flexible sortBy(comparing(f), xs) -- and uses a much faster ObjC NSArray sort method -- sortBy :: (a -> a -> Ordering) -> [a] -> [a] on sortBy(f, xs)

   if length of xs > 1 then
       set h to item 1 of xs
       set f to mReturn(f)
       script
           on |λ|(x)
               f's |λ|(x, h) ≤ 0
           end |λ|
       end script
       set lessMore to partition(result, rest of xs)
       sortBy(f, |1| of lessMore) & {h} & ¬
           sortBy(f, |2| of lessMore)
   else
       xs
   end if

end sortBy

-- splitOn :: String -> String -> [String] on splitOn(pat, src)

   set {dlm, my text item delimiters} to ¬
       {my text item delimiters, pat}
   set xs to text items of src
   set my text item delimiters to dlm
   return xs

end splitOn

-- swap :: (a, b) -> (b, a) on swap(ab)

   if class of ab is record then
       Tuple(|2| of ab, |1| of ab)
   else
       {item 2 of ab, item 1 of ab}
   end if

end swap

-- take :: Int -> [a] -> [a] -- take :: Int -> String -> String on take(n, xs)

   set c to class of xs
   if list is c then
       if 0 < n then
           items 1 thru min(n, length of xs) of xs
       else
           {}
       end if
   else if string is c then
       if 0 < n then
           text 1 thru min(n, length of xs) of xs
       else
           ""
       end if
   else if script is c then
       set ys to {}
       repeat with i from 1 to n
           set v to xs's |λ|()
           if missing value is v then
               return ys
           else
               set end of ys to v
           end if
       end repeat
       return ys
   else
       missing value
   end if

end take

-- toLower :: String -> String on toLower(str)

   set ca to current application
   ((ca's NSString's stringWithString:(str))'s ¬
       lowercaseStringWithLocale:(ca's NSLocale's currentLocale())) as text

end toLower

-- Tuple (,) :: a -> b -> (a, b) on Tuple(a, b)

   {type:"Tuple", |1|:a, |2|:b, length:2}

end Tuple

-- tupleFromList :: [a] -> (a, a ...) on tupleFromList(xs)

   set lng to length of xs
   if 1 < lng then
       if 2 < lng then
           set strSuffix to lng as string
       else
           set strSuffix to ""
       end if
       script kv
           on |λ|(a, x, i)
               insertMap(a, (i as string), x)
           end |λ|
       end script
       foldl(kv, {type:"Tuple" & strSuffix}, xs) & {length:lng}
   else
       missing value
   end if

end tupleFromList

-- unQuoted :: String -> String on unQuoted(s)

   script p
       on |λ|(x)
           --{34, 39} contains id of x
           34 = id of x
       end |λ|
   end script
   dropAround(p, s)

end unQuoted

-- unzip :: [(a,b)] -> ([a],[b]) on unzip(xys)

   set xs to {}
   set ys to {}
   repeat with xy in xys
       set end of xs to |1| of xy
       set end of ys to |2| of xy
   end repeat
   return Tuple(xs, ys)

end unzip

-- words :: String -> [String] on |words|(s)

   set ca to current application
   (((ca's NSString's stringWithString:(s))'s ¬
       componentsSeparatedByCharactersInSet:(ca's ¬
           NSCharacterSet's whitespaceAndNewlineCharacterSet()))'s ¬
       filteredArrayUsingPredicate:(ca's ¬
           NSPredicate's predicateWithFormat:"0 < length")) as list

end |words|</lang>

Output:

"[('july', '16')]"

Common Lisp

<lang lisp>

Author

Amir Teymuri, Saturday 20.10.2018

(defparameter *possible-dates*

 '((15 . may) (16 . may) (19 . may)
   (17 . june) (18 . june)
   (14 . july) (16 . july)
   (14 . august) (15 . august) (17 . august)))

(defun unique-date-parts (possible-dates &key (alist-look-at #'car) (alist-r-assoc #'assoc))

 (let* ((date-parts (mapcar alist-look-at possible-dates))	 

(unique-date-parts (remove-if #'(lambda (part) (> (count part date-parts) 1)) date-parts)))

   (mapcar #'(lambda (part) (funcall alist-r-assoc part possible-dates))
   	    unique-date-parts)))

(defun person (person possible-dates)

 "Who's turn is it to think?"
 (case person
   ('albert (unique-date-parts possible-dates :alist-look-at #'cdr :alist-r-assoc #'rassoc))
   ('bernard (unique-date-parts possible-dates :alist-look-at #'car :alist-r-assoc #'assoc))))

(defun cheryls-birthday (possible-dates)

 (person 'albert			

(person 'bernard (set-difference possible-dates (person 'bernard possible-dates) :key #'cdr))))

(cheryls-birthday *possible-dates*) ;; => ((16 . JULY)) </lang>

F#

<lang fsharp> //Find Cheryl's Birthday. Nigel Galloway: October 23rd., 2018 type Month = |May |June |July |August let fN n= n |> List.filter(fun (_,n)->(List.length n) < 2) |> List.unzip let dates = [(May,15);(May,16);(May,19);(June,17);(June,18);(July,14);(July,16);(August,14);(August,15);(August,17)] let _,n = dates |> List.groupBy snd |> fN let i = n |> List.concat |> List.map fst |> Set.ofList let _,g = dates |> List.filter(fun (n,_)->not (Set.contains n i)) |> List.groupBy snd |> fN let _,e = List.concat g |> List.groupBy fst |> fN printfn "%A" e </lang>

Output:

[[(July, 16)]]

Go

<lang go>package main

import (

   "fmt"
   "time"

)

type birthday struct{ month, day int }

func (b birthday) String() string {

   return fmt.Sprintf("%s %d", time.Month(b.month), b.day)

}

func (b birthday) monthUniqueIn(bds []birthday) bool {

   count := 0
   for _, bd := range bds {
       if bd.month == b.month {
           count++
       }
   }
   if count == 1 {
       return true
   }
   return false

}

func (b birthday) dayUniqueIn(bds []birthday) bool {

   count := 0
   for _, bd := range bds {
       if bd.day == b.day {
           count++
       }
   }
   if count == 1 {
       return true
   }
   return false

}

func (b birthday) monthWithUniqueDayIn(bds []birthday) bool {

   for _, bd := range bds {
       if bd.month == b.month && bd.dayUniqueIn(bds) {
           return true
       }
   }
   return false

}

func main() {

   choices := []birthday{
       {5, 15}, {5, 16}, {5, 19}, {6, 17}, {6, 18},
       {7, 14}, {7, 16}, {8, 14}, {8, 15}, {8, 17},
   }

   // Albert knows the month but doesn't know the day.
   // So the month can't be unique within the choices.
   var filtered []birthday
   for _, bd := range choices {
       if !bd.monthUniqueIn(choices) {
           filtered = append(filtered, bd)
       }
   }

   // Albert also knows that Bernard doesn't know the answer.
   // So the month can't have a unique day.
   var filtered2 []birthday
   for _, bd := range filtered {
       if !bd.monthWithUniqueDayIn(filtered) {
           filtered2 = append(filtered2, bd)
       }
   }

   // Bernard now knows the answer.
   // So the day must be unique within the remaining choices.
   var filtered3 []birthday
   for _, bd := range filtered2 {
       if bd.dayUniqueIn(filtered2) {
           filtered3 = append(filtered3, bd)
       }
   }

   // Albert now knows the answer too.
   // So the month must be unique within the remaining choices.
   var filtered4 []birthday
   for _, bd := range filtered3 {
       if bd.monthUniqueIn(filtered3) {
           filtered4 = append(filtered4, bd)
       }
   }

   if len(filtered4) == 1 {
       fmt.Println("Cheryl's birthday is", filtered4[0])
   } else {
       fmt.Println("Something went wrong!")
   }

}</lang>

Output:

Cheryl's birthday is July 16

Haskell

<lang haskell>{-# LANGUAGE OverloadedStrings #-}

import Data.List as L (filter, groupBy, head, length, sortBy) import Data.Map.Strict as M (Map, fromList, keys, lookup) import Data.Text as T (Text, splitOn, words) import Data.Maybe (fromJust) import Data.Ord (comparing) import Data.Function (on) import Data.Tuple (swap)

data DatePart

 = Month
 | Day

type M = Text

type D = Text

main :: IO () main =

 print $
 -- The month with only one remaining day,
 --
 -- (A's month contains only one remaining day)
 -- (3 :: A "Then I also know")
 uniquePairing Month $
 
 -- among the days with unique months,
 --
 -- (B's day is paired with only one remaining month)
 -- (2 :: B "I know now")
 uniquePairing Day $
 
 -- excluding months with unique days,
 --
 -- (A's month is not among those with unique days)
 -- (1 :: A "I know that Bernard does not know")
 monthsWithUniqueDays False $
 
 -- from the given month-day pairs:
 --
 -- (0 :: Cheryl's list)
 (\(x:y:_) -> (x, y)) . T.words <$>
 splitOn
   ", "
   "May 15, May 16, May 19, June 17, June 18, \
             \July 14, July 16, Aug 14, Aug 15, Aug 17"

-- QUERY FUNCTIONS --------------------------------------------- monthsWithUniqueDays :: Bool -> [(M, D)] -> [(M, D)] monthsWithUniqueDays bln xs =

 let months = fst <$> uniquePairing Day xs
 in L.filter
      (\(m, _) ->
          (if bln
             then id
             else not)
            (m `elem` months))
      xs

uniquePairing :: DatePart -> [(M, D)] -> [(M, D)] uniquePairing dp xs =

 let f =
       case dp of
         Month -> fst
         _ -> snd
 in bindPairs
      xs
      (\md ->
          let dct :: M.Map Text [Text]
              dct = f md
              uniques =
                L.filter
                  ((1 ==) . L.length . fromJust . flip M.lookup dct)
                  (keys dct)
          in L.filter ((`elem` uniques) . f) xs)

bindPairs :: [(M, D)]

         -> ((M.Map Text [Text], M.Map Text [Text]) -> [(M, D)])
         -> [(M, D)]

bindPairs xs f = f (mapFromPairs xs, mapFromPairs (swap <$> xs))

mapFromPairs :: [(M, D)] -> Map Text [Text] mapFromPairs xs =

 M.fromList $
 ((,) . fst . L.head) <*> fmap snd <$>
 L.groupBy (on (==) fst) (L.sortBy (comparing fst) xs)</lang>

Output:

[("July","16")]

JavaScript

<lang javascript>(() => {

   'use strict';

   // main :: IO ()
   const main = () => {
       const
           month = fst,
           day = snd;
       showLog(
           map(x => Array.from(x), (

               // The month with only one remaining day,

               // (A's month contains only one remaining day)
               // (3 :: A "Then I also know")
               uniquePairing(month)(

                   // among the days with unique months,

                   // (B's day is paired with only one remaining month)
                   // (2 :: B "I know now")
                   uniquePairing(day)(

                       // excluding months with unique days,

                       // (A's month is not among those with unique days)
                       // (1 :: A "I know that Bernard does not know")
                       monthsWithUniqueDays(false)(

                           // from the given month-day pairs:

                           // (0 :: Cheryl's list)
                           map(x => tupleFromList(words(strip(x))),
                               splitOn(/,\s+/,
                                   `May 15, May 16, May 19,
                                       June 17, June 18, July 14, July 16,
                                       Aug 14, Aug 15, Aug 17`
                               )
                           )
                       )
                   )
               )
           ))
       );
   };

   // monthsWithUniqueDays :: Bool -> [(Month, Day)] -> [(Month, Day)]
   const monthsWithUniqueDays = blnInclude => xs => {
       const months = map(fst, uniquePairing(snd)(xs));
       return filter(
           md => (blnInclude ? id : not)(
               elem(fst(md), months)
           ),
           xs
       );
   };

   // uniquePairing :: ((a, a) -> a) ->
   //      -> [(Month, Day)] -> [(Month, Day)]
   const uniquePairing = f => xs =>
       bindPairs(xs,
           md => {
               const
                   dct = f(md),
                   matches = filter(
                       k => 1 === length(dct[k]),
                       Object.keys(dct)
                   );
               return filter(tpl => elem(f(tpl), matches), xs);
           }
       );

   // bindPairs :: [(Month, Day)] -> (Dict, Dict) -> [(Month, Day)]
   const bindPairs = (xs, f) => f(
       Tuple(
           dictFromPairs(fst)(snd)(xs),
           dictFromPairs(snd)(fst)(xs)
       )
   );

   // dictFromPairs :: ((a, a) -> a) -> ((a, a) -> a) -> [(a, a)] -> Dict
   const dictFromPairs = f => g => xs =>
       foldl((a, tpl) => Object.assign(
           a, {
               [f(tpl)]: (a[f(tpl)] || []).concat(g(tpl).toString())
           }
       ), {}, xs);

   // GENERIC ABSTRACTIONS -------------------------------

   // Tuple (,) :: a -> b -> (a, b)
   const Tuple = (a, b) => ({
       type: 'Tuple',
       '0': a,
       '1': b,
       length: 2
   });

   // elem :: Eq a => a -> [a] -> Bool
   const elem = (x, xs) => xs.includes(x);

   // filter :: (a -> Bool) -> [a] -> [a]
   const filter = (f, xs) => xs.filter(f);

   // foldl :: (a -> b -> a) -> a -> [b] -> a
   const foldl = (f, a, xs) => xs.reduce(f, a);

   // fst :: (a, b) -> a
   const fst = tpl => tpl[0];

   // id :: a -> a
   const id = x => x;

   // intersect :: (Eq a) => [a] -> [a] -> [a]
   const intersect = (xs, ys) =>
       xs.filter(x => -1 !== ys.indexOf(x));

   // Returns Infinity over objects without finite length
   // this enables zip and zipWith to choose the shorter
   // argument when one is non-finite, like cycle, repeat etc

   // length :: [a] -> Int
   const length = xs =>
       (Array.isArray(xs) || 'string' === typeof xs) ? (
           xs.length
       ) : Infinity;

   // map :: (a -> b) -> [a] -> [b]
   const map = (f, xs) => xs.map(f);

   // not :: Bool -> Bool
   const not = b => !b;

   // showLog :: a -> IO ()
   const showLog = (...args) =>
       console.log(
           args
           .map(JSON.stringify)
           .join(' -> ')
       );

   // snd :: (a, b) -> b
   const snd = tpl => tpl[1];

   // splitOn :: String -> String -> [String]
   const splitOn = (pat, src) =>
       src.split(pat);

   // strip :: String -> String
   const strip = s => s.trim();

   // tupleFromList :: [a] -> (a, a ...)
   const tupleFromList = xs =>
       TupleN.apply(null, xs);

   // TupleN :: a -> b ...  -> (a, b ... )
   function TupleN() {
       const
           args = Array.from(arguments),
           lng = args.length;
       return lng > 1 ? Object.assign(
           args.reduce((a, x, i) => Object.assign(a, {
               [i]: x
           }), {
               type: 'Tuple' + (2 < lng ? lng.toString() : ),
               length: lng
           })
       ) : args[0];
   };

   // words :: String -> [String]
   const words = s => s.split(/\s+/);

   // MAIN ---
   return main();

})();</lang>

Output:

[["July","16"]]

Python

<lang python>from itertools import (groupby) from re import (split)

1. main :: IO ()

def main():

   (month, day) = (0, 1)
   print(
       # (A's month contains only one remaining day)
       # (3 :: A "Then I also know")
       uniquePairing(month)(
           # (B's day is paired with only one remaining month)
           # (2 :: B "I know now")
           uniquePairing(day)(
               # (A's month is not among those with unique days)
               # (1 :: A "I know that Bernard does not know")
               monthsWithUniqueDays(False)(
                   # 0 :: Cheryl's list:
                   list(map(
                       lambda x: tuple(x.split()),
                       split(
                           ', ',
                           'May 15, May 16, May 19, ' +
                           'June 17, June 18, ' +
                           'July 14, July 16, ' +
                           'Aug 14, Aug 15, Aug 17'
                       )
                   ))
               )
           )
       )
   )

1. QUERY FUNCTIONS ----------------------------------------

1. monthsWithUniqueDays :: Bool -> [(Month, Day)] -> [(Month, Day)]

def monthsWithUniqueDays(blnInclude):

   def go(xs):
       (month, day) = (0, 1)
       months = list(map(fst, uniquePairing(day)(xs)))
       return list(filter(
           lambda md: (
               id if blnInclude else _not
           )(md[month] in months),
           xs
       ))
   return lambda xs: go(xs)

1. uniquePairing :: Int -> [(Month, Day)] -> [(Month, Day)]

def uniquePairing(i):

   def go(xs):
       def inner(md):
           dct = md[i]
           uniques = list(filter(
               lambda k: 1 == len(dct[k]),
               dct.keys()
           ))
           return filter(lambda tpl: tpl[i] in uniques, xs)
       return inner
   return lambda xs: bindPairs(xs)(go(xs))

1. bindPairs
2. :: [(Month, Day)]
3. -> ((Dict String [String], Dict String [String]) -> [(Month, Day)])
4. -> [(Month, Day)]

def bindPairs(xs):

   return lambda f: list(f(
       (dictFromPairs(xs), dictFromPairs(map(swap, xs)))
   ))

1. dictFromPairs :: [(Month, Day)] -> Dict String [String]

def dictFromPairs(xs):

   return dict(
       (k, list(map(snd, m))) for k, m in groupby(
           sorted(xs, key=fst), key=fst
       )
   )

1. GENERIC -------------------------------------------------

1. fst :: (a, b) -> a

def fst(tpl):

   return tpl[0]

1. id :: a -> a

def id(x):

   return x

1. _not :: Bool -> Bool

def _not(bln):

   return not bln

1. snd :: (a, b) -> b

def snd(tpl):

   return tpl[1]

1. swap :: (a, b) -> (b, a)

def swap(tpl):

   return (tpl[1], tpl[0])

1. MAIN ---

main()</lang>

Output:

[('July', '16')]

Perl

<lang perl>sub filter {

   my($test,@dates) = @_;
   my(%M,%D,@filtered);

   # analysis of potential birthdays, keyed by month and by day
   for my $date (@dates) {
       my($mon,$day) = split '-', $date;
       $M{$mon}{cnt}++;
       $D{$day}{cnt}++;
       push @{$M{$mon}{day}},  $day;
       push @{$D{$day}{mon}},  $mon;
       push @{$M{$mon}{bday}}, "$mon-$day";
       push @{$D{$day}{bday}}, "$mon-$day";
   }

   # eliminates May/Jun dates based on 18th and 19th being singletons
   if ($test eq 'singleton') {
       my %skip;
       for my $day (grep { $D{$_}{cnt} == 1 } keys %D) { $skip{ @{$D{$day}{mon}}[0] }++    }
       for my $mon (grep { ! $skip{$_}      } keys %M) { push @filtered, @{$M{$mon}{bday}} }

   # eliminates Jul/Aug 14th because day count > 1 across months
   } elsif ($test eq 'duplicate') {
       for my $day (grep { $D{$_}{cnt} == 1 } keys %D) { push @filtered, @{$D{$day}{bday}} }

   # eliminates Aug 15th/17th because day count > 1, within month
   } elsif ($test eq 'multiple') {
       for my $day (grep { $M{$_}{cnt} == 1 } keys %M) { push @filtered, @{$M{$day}{bday}} }
   }
   return @filtered;

}

1. doesn't matter what order singleton/duplicate tests are run, but 'multiple' must be last;

my @dates = qw<5-15 5-16 5-19 6-17 6-18 7-14 7-16 8-14 8-15 8-17>; @dates = filter($_, @dates) for qw<singleton duplicate multiple>;

my @months = qw<_ January February March April May June July August September October November December>;

my ($m, $d) = split '-', $dates[0]; print "Cheryl's birthday is $months[$m] $d.\n";</lang>

Output:

Cheryl's birthday is July 16.

Perl 6

<lang perl6>my @dates =

   { :15day, :5month },
   { :16day, :5month },
   { :19day, :5month },
   { :17day, :6month },
   { :18day, :6month },
   { :14day, :7month },
   { :16day, :7month },
   { :14day, :8month },
   { :15day, :8month },
   { :17day, :8month }

1. Month can't have a unique day

my @filtered = @dates.grep(*.<month> != one(@dates.grep(*.<day> == one(@dates».<day>))».<month>));

1. Day must be unique and unambiguous in remaining months

my $birthday = @filtered.grep(*.<day> == one(@filtered».<day>)).classify({.<month>})\

   .first(*.value.elems == 1).value[0];

1. convenience array

my @months = < January February March April May June July August September October November December>;

say "Cheryl's birthday is { @months[$birthday<month>] } {$birthday<day>}.";</lang>

Output:

Cheryl's birthday is July 16.

zkl

<lang zkl>dates:=T(T("May", 15), T("May", 16), T("May", 19),

        T("June",  17), T("June",  18), 

T("July", 14), T("July", 16), T("August",14), T("August",15), T("August",17) ); mDs:=dates.pump(Dictionary().appendKV); // "June":(15,16,19), ... dMs:=dates.pump(Dictionary().appendKV,"reverse"); // 15:"May", 16:"May", 19:"May", ...

// remove unique days (18,19) --> "July":(14,16),"August":(14,15,17) dMs.values.apply2('wrap(ms){ if(ms.len()==1) mDs.del(ms[0]) });

// find intersection of above days --> (14) fcn intersection(l1,l2){ l1.pump(List,l2.holds,'==(True),Void.Filter) } badDs:=mDs.values.reduce(intersection);

// --> July:(16),August:(15,17) --> ( ("July",(16)) ) theDay:=mDs.filter('wrap([(m,ds)]){ ds.removeEach(badDs).len()==1 });

// print birthday such that muliples are shown, if any println("Cheryl's birthday is ",theDay.flatten().flatten().concat(" "));</lang>

Output:

Cheryl's birthday is July 16