Four men -- Aaron, Barry, Colin & David and four women -- Marie, Norma, Olive & Pearl -- attended a wedding.
- One of the four men married one of the four women.
- If neither Aaron nor Marie got married, then Olive got married.
- If neither Aaron nor Norma got married, then Barry got married.
- If neither Barry nor Olive got married, then Colin got married.
- If neither Colin nor Norma got married, then Marie got married.
Who got married?
I prefer to work with the contrapositives:
(2) If not O, then A or M
(3) If not B, then A or N
(4) If not C, then B or O
(5) If not M, then C or N
Assume B is not the groom. Then, from (3), A or N got married.
If A, then from (4) A must have married O.
But A & O contradicts 5.
If N, then from (2) N must have married A.
But N & A contradicts 4.
Therefore, our initial assumption is wrong, and B is the groom.
This satisfies (3) and (4), and the other two simplify to
(2) If not O, then M.
(5) If not M, then N.
One or both of the two predicates must be true, so the bride must be M or N. If N is the bride, then this contradicts (2), so N is not the bride. So M must be the bride.
Only solution: B & M were married.
Edited on May 3, 2013, 8:20 pm