Cheryl's birthday

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.

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