# If a chicken and a half can lay an egg and a half in a day and a half, how many hens to lay six eggs in six days?

Dear Cecil:

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.

Cecil replies:

"Think" is not the operative term here, Margo. Cecil knows. What he knows in this instance is that you're right and Marilyn is wrong. 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 1-1/2 hens (your answer), not one (Marilyn's answer). And no excuses 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.

**Ha!**

In Marilyn vos Savant's "Ask Marilyn" column in the July 1, 1990 *Parade* magazine, a reader gives essentially the answer above, to which Ms. Savant replies:

Good catch, you guys! Those of you who said "one and a half hens" are right, and my "one hen" is wrong.... And here I'd always assumed this was one of those "How much wood would a woodchuck chuck?" kind of tongue twisters! It's actually a logic puzzle.