A Straight Dope Classic from Cecil's Storehouse of Human Knowledge

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?

June 29, 1990

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.

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