The Viral 1903 Math Puzzle That Stumped America: How Old Is Ann?
I explore the history of a notorious arithmetic riddle from 1903 that captivated the United States, leading to widespread confusion and humorous misinterpretations. Originally published in the New York World, the problem regarding the ages of Mary and Ann sparked a national frenzy, inspiring songs, plays, and satirical responses. This piece examines how a simple question baffled prominent figures and became a cultural phenomenon comparable to modern viral puzzles.
The amount and quality of intelligence utilized in the working out of cross-word puzzles almost precisely equal those that were revealed some years ago when an amazing — and discouraging — army of Americans filled the newspapers that cater to such folk with triumphant solutions of an arithmetical problem concerning the age of a supposititious Ann.
- losvedir
I don't know why but I really struggled to internalize what the question was asking. Here's my take on a rewrite that's clearer:
Mary is 24, which is twice as old as Ann was some time ago. At that time, Mary was the age that Ann is now. What is that age?
- judofyr
Rephrasing it makes it easier to grasp:
Mary is 24 years old. When Mary was Ann’s current age, Ann was 12 years old (half Mary’s current age).
This makes it a bit easier to realize that Ann’s age has to be right in the middle of 12 and 24.
- HarHarVeryFunny
Ann is 18.
I think what makes it confusing is the "variable overloading" referring to both the current ages of Mary and Ann (M & A), and their ages at some point in the past "when Mary was as old as Ann is now" (M' & A').
So, what we're given is:
M = 24
M' = A
M = 2A' => A' = M/2 = 12
Since the age gap between Mary and Ann is constant, we know:
M - A = M'- A'
So, substituting in the known values:
24 - A = A - 12
2A = 36
A = 18
We can double check the result. Since Mary (24) is 6 years older than Ann (18), then when Mary was 18 Ann would have been 12, so Mary is now twice that age as given.
- pkasting
The closing problem is more fun.
> A man is twice the age his wife was when he was the age she is now. When she reaches his present age, their combined years will be 100. Find the age of each.
This seemed initially like something amenable to guessing and checking a few ratios. <narrator voice>It was not.</narrator voice>
My answer: The man is 44 4/9 years old, the wife 33 1/3 years.
- anigbrowl
It's amazing to me how much effort people invest in elaborating wrong answers.
The key insight here is to remember that time moves the same for both Mary and Ann. Let's call the number of years between past and present X. Then
24 - X = 12 + X => 24 - 12 = 2X => X = 6.