Horace has decided that he will marry one of the three ladies - Alice, Beatrice and Candice.

[1] Of Alice and Beatrice:
(a) Either both have hazel eyes or both do not.
(b) One is red-haired and the other is not.

[2] Of Alice and Candice:
(a) Either both are red-haired or both are not.
(b) One is slender and the other is not.

[3] Of Beatrice and Candice:
(a) One has hazel eyes and the other does not.
(b) One is slender and the other is not.

[4] Of the mentioned characteristics - hazel eyes, red-haired, and slender:
(a) If any of Alice, Beatrice, and Candice has exactly two of these characteristics, then Horace will marry only the lady with the least number of them.
(b) If any of Alice, Beatrice, and Candice has exactly one of these characteristics, then Horace will marry only the woman with the greatest number of them.

Which one of the ladies will Horace marry?

Let's assume that Alice has hazel eyes, red hair, and is slender.  Then:

From 1a, Beatrice has hazel eyes.

From 1b, Beatrice does NOT have red hair.

From 2a, Candice has red hair.

From 2b, Candice is NOT slender.

From 3a, Candice does NOT have hazel eyes.

From 3b, Beatrice is slender.

So Alice has 3 of the characteristics, Beatrice has 2, and Candice has 1.

From 4a, Beatrice has exactly two of these characteristics, so Horace will marry Candice (the woman with the least of them).

From 4b, Candice has exactly one of these characteristics, so Horace will marry Alice (the woman with the most of them).

This is a contradiction.  Am I misunderstanding something?

 

Posted by tomarken on 2014-07-09 16:19:55