I am enclosing a copy of a recent column in Parade magazine by Marilyn vos Savant, who supposedly is listed in the "Guinness Book of World Records Hall of Fame" for "highest IQ." A writer asks Marilyn for an answer to the following riddle:
If a hen and a half can lay an egg and a half in a day and a half, how many hens does it take to lay six eggs in six days?
Marilyn answers as follows:
"My father loved this one too, but I didn't get it then, and I don't get it now. What's the problem? Is "one hen' too obvious? If a hen and a half can lay an egg and a half, etc., that means a hen can lay an egg in a day. And if just one hen lays one egg a day for six days, we'd have six eggs right there, wouldn't we?"
I'm quite sure this is incorrect and that the answer is one and a half hens. What do you think? I've enclosed a copy of my solution. --Margo Carraher-Sommer, Chester, Virginia
Just goes to show you, Margo, you can have a high IQ and still be a mope. Cecil has always been bugged by this Marilyn vos Savant person, who writes a column he considers a pale shadow of his own. Some days I have half a mind to take an IQ test myself, just to knock her out of Guinness. But hey, some people need these little ego props.
Anyway, you're right and Marilyn is wrong. Obviously she didn't get the riddle because she didn't bother to think about it. If you'll permit me to adapt your solution a bit, we can put the basic proposition this way:
1 1/2 hens x 1 1/2 days x rate per hen per day = 1 1/2 eggs
We convert the fractions thus:
3/2 hens x 3/2 days x rate per hen per day = 3/2 eggs
To get rid of the fractions, Marilyn vos Savant presumably multiplies both sides by 2/3 to get:
1 hen x 1 day x rate per hen per day = 1 egg
Rate per hen per day = 1 egg
As a moment's study will make clear, however, Marilyn has done her algebra wrong. If you multiply both sides by 2/3 what you really get is:
1 hen x 3/2 days x rate per hen per day = 1 egg
3/2 rate per hen per day = 1 egg
Rate per hen per day = 2/3 egg
In other words, a hen lays an egg every day and a half, or four eggs in six days. If you want six eggs in six days, therefore, you need 1 1 hens (your answer), not one (Marilyn's answer). And don't give me that crap about how half a hen can't lay anything--we're talking science here. Marilyn vos Savant, by way of contrast, is talking off the top of her head.
I was amused to read your comments and reader reaction concerning slugs in More of the Straight Dope. If you thought these terrestrial pulmonate gastropods were disgusting before, get a load of the following, from Cascade Olympic Natural History by Daniel Mathews:
"Banana slugs are notorious for chewing off their penises to conclude mating (both partners chew), probably because their unusually large organs are more difficult for them to withdraw than to regenerate later. . . . To make themselves recognizable, the species have evolved a bizarre assortment of palpable structures--sharp little jabbing needles, delicately branched sperm packets, and overdeveloped penises, all with dimensions peculiar to the species. Banana slug penises are large, but nothing like those of one rare race in the Alps--32 1-inch tumescences dangling from 6-inch slugs. --N.B. Spickard, Mercer Island, Washington
That's just great, N.B. Now excuse me while I go to the chapel to pray for your heathen soul.
Art accompanying story in printed newspaper (not available in this archive): illustration/Slug Signorino.