bout de papier, Vol. 7, No. 4 (1990), p. 48
“It’s absurd, Liebnitz,” growled Chief Inspector de Toombs. “We have these four sisters with the maiden name of Hath – Beth, Barbara, Beulah and Brandy. We know that they are each married to one of a set of identical quadruplets named Streep — David, Donald, Duff and Duncan. One of the husbands has been murdered, but we can’t tell which. The sisters won’t say anything about the crime, or anything else except their names and the fact that each of the sisters has a different age (all ages are in whole years). Since we don’t know where they’re from, we can’t check up on them.”
“We know that one is the murderess, another is the victim’s wife (who paid for the crime) and a third witnessed the killing, de Toombs went on. “These three we could convict of murder and conspiracy, if we knew which they were. But the fourth sister is a private eye who had nothing to do with the murder. It’s only misguided loyalty that’s keeping her silent. I have to know which one she is before I turn the case over to the Crown.”
“Surely you must have more information than that,” protested the logician. “Clues from their belongings, perhaps, or from the scene of the crime.”
“Unfortunately not,” replied the embarrased policeman. “My assistant, the late Inspector Sellers, accidentally put the file in a closet with a bombe in it. It was last seen in orbit around Carl Sagan. We do have one thing that the Inspector gave to a Toulouse- Lautrec look-alike. It’s his notes on a series of statements, one made by each sister to each other sister, when we put them together two by two. Here’s the list, Liebnitz.
(1) Barbara to Beulah: Either Duncan is the victim or Dave is
married to the youngest of us sisters, but not both.
(2) Beulah to Brandy: I am not married to Donald.
(3) Brandy to Barbara: Beth always lies.
(4) Barbara to Beth: The witness is exactly 50% older than you
are.
(5) Beth to Beulah: Donald is married either to you or to the oldest
of us sisters.
(6) Beulah to Barbara: One of us sisters is seven years older than
one of the others, and the youngest of us is 24.
(7) Brandy to Beulah: The murderess is not married to Duff.
(8) Barbara to Brandy: You and I are older than the detective
by one and six years, not necessarily in that order.
(9) Beulah to Beth: You always lie.
(10) Beth to Barbara: I always lie.
(11) Beth to Brandy: The murderess is either Duff’s wife or the
youngest of us sisters, but not both.
(12) Brandv to Beth: Mv hushand was not the victim.
“Well, that certainly should be enough to solve the case,” concluded Liebnitz after reading the list. “Let’s see….
“Just one more thing you should know,” interjected de Toombs ruefully. “Before he died, the victim said that one of the sisters always tells the truth, one always lies, one is totally undependable and the fourth matches the habits of the person she’s talking to — she lies to the liar, tells the truth to the truthful sister, and mixes truth and lies at random with the undependable one.”
“Oh great!” sighed the logician. “And given the stakes involved, having one of the sisters mention the witness or the murderess or the detective doesn’t necessarily mean that she herself isn’t that character. Still, if we assume that the victim’s deathbed statement was the truth…yes, I think I can still give you a solution.”
“If you can, I’ll eat my hat!” exclaimed the Chief Inspector.
But LDC proved equal to his claim. Can you duplicate his feat by identifying each sister’s husband, age and role in the murder (murderess, witness, victim’s wife or detective). Can you say which is the truthful sister, the liar, the undependable sister and the matcher? Finally, can you recommend whether sauce bearnaise or sauce diable goes better with a fedora?
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Originally published in bout de papier, Vol. 7, No. 4 (1990), p. 48. Read the rest of this issue →
