+This logic puzzle has been floating around the internet lately. When I +caught wind of it, I thought it would be a great exercise to tackle +using Prolog. I'm not especially good with the language yet, so it +added to the challenge a bit, but it was a pretty worthwhile +undertaking. When I got stumped, I discovered that mapping out the +birthdays into a grid helped me visualize the problem and ultimately +solve it, so I've included that with my prolog code so you can see how +I arrived at the answer. +
+ ++Albert and Bernard have just met Cheryl. “When is your birthday?” +Albert asked Cheryl. Cheryl thought for a moment and said, “I won’t +tell you, but I’ll give you some clues”. She wrote down a list of +ten dates: +
+ + ++“One of these is my birthday,” she said. +
+ + ++Cheryl whispered in Albert’s ear the month, and only the month, of +her birthday. To Bernard, she whispered the day, and only the +day. “Can you figure it out now?” she asked Albert. +
+ + ++Albert: “I don’t know when your birthday is, but I know Bernard +doesn’t know, either.” +
+ ++Bernard: “I didn’t know originally, but now I do.” +
+ ++Albert: “Well, now I know, too!” +
+ ++When is Cheryl’s birthday? +
++To start off, i entered each of the possible birthdays as facts: +
+ +possible_birthday(may, 15). +possible_birthday(may, 16). +possible_birthday(may, 19). +possible_birthday(june, 17). +possible_birthday(june, 18). +possible_birthday(july, 14). +possible_birthday(july, 16). +possible_birthday(august, 14). +possible_birthday(august, 15). +possible_birthday(august, 17). ++
+And here they are, mapped out in a grid: +
+ +| + | May | +June | +July | +August | +
|---|---|---|---|---|
| 14 | ++ | + | X | +X | +
| 15 | +X | ++ | + | X | +
| 16 | +X | ++ | X | ++ |
| 17 | ++ | X | ++ | X | +
| 18 | ++ | X | ++ | + |
| 19 | +X | ++ | + | + |
++ ++I don’t know when your birthday is,… +
+
+Albert only knows the month, and the month isn't enough to uniquely +identify Cheryl's birthday. +
+ +month_is_not_unique(M) :- + bagof(D, possible_birthday(M, D), Days), + length(Days, Len), + Len > 1. ++
++ ++… but I know Bernard doesn’t know, either. +
+
+Albert knows that Bernard doesn't know Cheryl's +birthday. Therefore, the day alone isn't enough to know Cheryl's +birthday, and we can infer that the month of Cheryl's birthday does +not include any of the unique dates. +
+ +day_is_not_unique(D) :- + bagof(M, possible_birthday(M, D), Months), + length(Months, Len), + Len > 1. + +month_has_no_unique_days(M) :- + forall(possible_birthday(M,D), + day_is_not_unique(D)). ++
+Based on what Albert knows at this point, let's see how we've +reduced the possible dates: +
+ +part_one(M,D) :- + possible_birthday(M,D), + month_is_not_unique(M), + month_has_no_unique_days(M), + day_is_not_unique(D). ++
+Results = [ (july, 14), (july, 16), (august, 14), (august, 15), (august, 17)]. ++ +
+So the unique days (the 18th and 19th) are out, as are the months +that contained them (May and June). +
+ +| + | July | +August | +
|---|---|---|
| 14 | +X | +X | +
| 15 | ++ | X | +
| 16 | +X | ++ |
| 17 | ++ | X | +
++ ++I didn’t know originally, but now I do. +
+
+For Bernard to know Cheryl's birthday, the day he knows must be +unique within the constraints we have so far. +
+ +day_is_unique(Month, Day) :- + findall(M, part_one(M, Day), [Month]). +part_two(Month, Day) :- + possible_birthday(Month, Day), + day_is_unique(Month, Day). ++
+Results = [ (july, 16), (august, 15), (august, 17)]. ++ +
+Both July and August contain the 14th, so that row is out. +
+ +| + | July | +August | +
|---|---|---|
| 15 | ++ | X | +
| 16 | +X | ++ |
| 17 | ++ | X | +
++ ++Well, now I know, too! +
+
+Albert's month must be the remaining unique month: +
+ +month_is_not_unique(Month, Day) :- + findall(D, part_two(Month, D), [Day]). +part_three(Month, Day) :- + possible_birthday(Month, Day), + month_is_not_unique(Month, Day). ++
+Results = [ (july, 16)]. ++ +
+August had two possible days, so it's now clear that the only +possible unique answer is July 16th. +
+ +| + | July | +
|---|---|
| 15 | ++ |
| 16 | +X | +
| 17 | ++ |
cheryls_birthday(Month, Day) :- + part_three(Month, Day). ++
+Month = july, +Day = 16. ++ +
+So, there we have it. Cheryl's birthday is July 16th! +
+ +| + | July | +
|---|---|
| 16 | +X | +