The Mystery of Ann's Age

Originally discussed by Arthur O'Dwyer

Reflecting on a piece from the New York Times dated November 17, 1924, the author notes a biting commentary on American intelligence. The article lamented that the same mental capacity used for crossword puzzles was previously displayed by a "discouraging" number of citizens who struggled with a simple arithmetic riddle. According to the Times, any competent eighth-grader should have been able to solve this problem mentally in roughly thirty seconds.

O'Dwyer muses that as he ages, the phrase "some years ago" increasingly feels appropriate even when it refers to events from two decades prior.

🧩 The Riddle

The puzzle, which likely debuted in the New York World around October 9, 1903, is stated as follows:

Mary is 24 years old. She is twice as old as Ann was when Mary was as old as Ann is now.

To put this into a more formal mathematical structure, we can let $M$ be Mary's current age and $A$ be Ann's current age. The "time gap" between them is $M - A$.

$M = 2 \times (A - (M - A))$

Breaking Down the Logic

To solve this, one must track the ages across two different points in time:

Steps to solve:

• Identify Mary's current age (24).
• Determine the age Ann was in the past (Half of 24 = 12).
• Calculate the difference between Mary's current age and Ann's past age.
• Apply that difference to find Ann's current age.

🎭 A Cultural Phenomenon

The problem wasn't just a math exercise; it became a national obsession. The New York Evening Post noted that the "Ann and Mary" conundrum captured the public's imagination more than almost anything since the "Pigs in Clover" craze.

The riddle permeated various media:

• Theater: A play by Barney Gerard featured Ann as a rebellious girl who avoided school. The plot centered on the authorities' struggle to determine her age to punish her.
• Music: Frank Daniels performed a song titled "How Old Is Ann?" at the Victoria Theatre. The audience hoped for a solution in the lyrics, but the song teased them instead.
• Politics: The cartoonist Ed F. Flinn even linked Ann to the secession of Panama.

The World eventually attributed the creation of the puzzle to a Mr. Perkin Warbeck from Newark, New Jersey.

❌ The Hall of Wrong Answers

Many "prominent" citizens attempted to solve the puzzle, often with disastrous results. Some simply misread the prompt, while others succumbed to total confusion.

The "Logic" of the Confused

Some responses were so erratic they bordered on performance art. For instance, the Kansas Journal correspondent argued: Ann is as old now as Mary was when Mary was half as old as her present age less the age of Ann...

Meanwhile, the Wyoming Tribune insisted the answer was 16, arguing that since Mary is 24 (four times six), dividing by six gives four, and somehow that leads to 16.

✍️ The Poet's Lament

The Washington Times shared a poem from an anonymous writer who suffered a mental breakdown attempting to solve the riddle:

I used to be contented and took comfort in my life, I dwelt in deep placidity, removed from care and strife, I never worried as I jogged along my even way, I worked a bit, I slept a bit, and still had time for play; I never had such things as nerves; my brain was clear and cool, But now I am a nervous wreck, and soon will be a fool.

It came about in this wise: One fell day a genial friend, Whose mind is full of whist and chess and problems without end, Propounded in a guileless way a problem which, to scan, Seemed simple: All you had to do was find the age of Ann.

Now, Ann is Mary’s sister, which you’ve no doubt heard before, And Mary— it is impolite, but Mary’s twenty-four. Now, Mary’s twenty-four, and she is twice as old today As Ann was when her sister was — that is, of course, to say, When Mary was — as old as Mary’s sister Ann