# Which sister to marry? [duplicate]

Tomorrow you will meet three sisters, and be married to one of them. The eldest always tells the truth, the youngest always lies. The middle sister lies or tells the truth at random. Knowing this, you would like to marry the either the eldest or the youngest—so you'll know where you stand.

Conscious to their own futures, the sisters conspire to visit you the night before. Everyone gets on really well. They are Abigail, Eleanor and Lucy. You're too polite to guess their ages. As they're about to leave, Abigail draws you aside and says 'since we might be married tomorrow, is there anything you'd like to ask?'. From the look in her eyes, you understand it should be a yes-no question. To achieve your aim, what do you ask?

Needless to say, the sisters know each others' ages.

Hint:

It might help to solve this simpler problem first Two doors with two guards - one lies, one tells the truth

## marked as duplicate by skv, Rob Watts, wbogacz, d'alar'cop, warspykingNov 8 '14 at 12:23

• What happens if she doesn't know the answer? – TheRubberDuck Nov 8 '14 at 1:18
• Good question, +1 – Kenshin Nov 8 '14 at 4:41
• @Mew it's a duplicate. – warspyking Nov 8 '14 at 12:27
• You're right, that puzzle is equivalent. I like to think my exposition is better written, but I don't suppose that matters here :/ – Colonel Panic Nov 10 '14 at 17:17
• The logic is a duplicate of the other question, but I agree the exposition of this one is better. Also, Mew's answer is simple; this version is easier to explain than the other. – user3294068 Nov 10 '14 at 17:25

You simply need to ask Abigail:

"Is Lucy older than Eleanor?"

Marry the sister she indicates as younger.

Explanation:

• If Abigail is the eldest: She is telling the truth, and so marrying the person she indicates as the youngest is marrying the person who is always lying, which is acceptable.
• If Abigail is the middle aged: Then it is acceptable to marry either of the other two girls, and thus marrying the one who Abigail selects as the youngest is permitted.
• If Abigail is the youngest: She is lying and thus the person she indicates is the youngest is in fact the eldest and therefore is the truth telling sister.

So overall, if you always pick the one Abigail chooses as the youngest then you will be marrying either the oldest or the youngest as you desire.

• I don't know why but for some reason I just don't like this answer... – warspyking Nov 8 '14 at 12:36
• I had to retract my upvote, you can do the same with mine if you like, but there'd something in the wording here I don't like, even after editing out the useless ending. – warspyking Nov 8 '14 at 12:39
• Why would you think that? The only other language I know is Lua and that's a scripting language. – warspyking Nov 8 '14 at 12:43
• @warspyking, This is the first time I have ever seen a puzzle like this so I wouldn't know about other versions of it. All I know is that they are sisters, clearly they know each others age. – Kenshin Nov 8 '14 at 13:30
• @warspyking Party pooper! This is a brilliant answer. – Rand al'Thor Mar 14 '15 at 23:18

Name the sisters A, B and C. A is the one who came to you. You now ask her:

"You are the oldest $\oplus$ B is the middle sister?"

If you get back the answer yes, then B is either the youngest or the oldest - pick B.

If you get back the answer no, then C is either the youngest or the oldest - pick C.

This hinges on the fact that A came to you and if you discard her, at least one of the others is "safe to marry".

If A was the middle sister, then regardless of yes/no whoever else you choose is "safe to marry".

If A was the oldest then she'll respond yes if B is safe and no if C is safe.

If A was the youngest then she'll respond yes if B is safe and no if C is safe.

$\oplus$ means logical XOR

• What the heck does "⊕" mean and how do you pronounce it when asking her the question? – warspyking Nov 8 '14 at 3:04
• It's logical XOR. You'd say "exor" maybe. – d'alar'cop Nov 8 '14 at 3:06
• Well I think my answer is much easier to use in an actual conversation... – warspyking Nov 8 '14 at 4:07
• @warspyking, and my answer is easier yet again. – Kenshin Nov 8 '14 at 4:26
• @Mew that doesn't make mine any less correct. – warspyking Nov 8 '14 at 4:30

Question:

Are one, and only one of these 2 statements true:

You are the eldest
Lucy is the middle aged/random

Response:

Yes: Lucy is safe to marry no matter what, feel free to check the possibilities.

No: Eleanor is safe to marry no matter what, feel free to check the possibilities