The simple math problem you can’t solve

“For every complex problem, there is an answer that is clear, simple, and wrong.”

— H. L. Mencken

I was recently introduced to a math problem that is so simple yet so crafty that I can only describe it as genius.

This problem gained some notoriety in 2018 when it stormed the internet.

The problem was part of a Chinese fifth-grade math class quiz.

Translated into English, the mind-bender reads:

“If a ship had 26 sheep and 10 goats onboard, how old is the ship’s captain?”

If you are as baffled as many are upon reading the question, go ahead and reread it.

That probably did not help, nor will multiple closer readings.

Where did this problem come from?

Gustave Flaubert is a French novelist best known for his debut novel, the classic Madame Bovary.

Flaubert was a perfectionist and was known for literary realism. He avoided the inexact, the abstract, and the cliché. Modern masters such as Kafka, Coetzee, and Nabokov were influenced by his lean and precise writing style.

In a letter to his sister Caroline in 1841, Flaubert posed the following question:

“Puisque tu fais de la géométrie et de la trigonométrie, je vais te donner un problème : Un navire est en mer, il est parti de Boston chargé de coton, il jauge 200 tonneaux. Il fait voile vers le Havre, le grand mât est cassé, il y a un mousse sur le gaillard d’avant, les passagers sont au nombre de douze, le vent souffle N.-E.-E., l’horloge marque 3 heures un quart d’après-midi, on est au mois de mai…. On demande l’âge du capitaine?”

Translated into English, the passage reads:

“Since you are now studying geometry and trigonometry, I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. It is the month of May. How old is the Captain?”

See it?

Genius, right?

140 years after Flaubert posed this question, a group of French researchers from Institut De Recherche Sur L’Enseignement Des Mathematiques De Grenoble (IREM) posed the question in its modern form to students 9 to 10 years old:

“On the boat, there are 26 sheep and 10 goats. What is the age of the Captain?”

This is essentially the same question posed in the Chinese classroom!

Shortly afterward, the researchers at IREM replicated this experiment on a larger scale. Six variations of the problem about the Captain’s age, for example: 

“There are 125 sheep and 5 dogs in a flock. How old is the shepherd?” 

“I have 4 lollies in my right pocket and 9 sweeties in my left pocket. How old is my father?” 

How those students and subsequent commentators approached the problem illustrates challenges in modern problem-solving and education.

Solutions Proposed

The problems did not gain much attention until it was posed to those Chinese math students. 

Maybe it’s due to the way social media works and the ability it creates to attract a larger audience. Or perhaps it’s just the inherent craftiness of the problem. Or maybe the timing was just right. Whatever the cause, it became a viral internet sensation.

The problem gained notoriety for the debate it stirred and the variety of creative approaches proposed.

The French researchers found more than three-quarters of the students used the addition of the numerical data from the assignment. They got a lot of 26 and 36 as answers.

Those are wrong.

One Chinese student claimed the Captain was 18 because they had to be an adult to drive the ship.

The internet was a lot more creative.

“The total weight of 26 sheep and 10 goat is 7,700kg, based on the average weight of each animal,” said one Weibo commenter.

“In China, if you’re driving a ship that has more than 5,000kg of cargo you need to have possessed a boat license for five years. The minimum age for getting a boat’s license is 23, so he’s at least 28.”

Wrong also.

What’s impressive about the dialogue that ensued was the vigorous debate about how to solve the problem. 

A minority of commenters claimed it was unsolvable.

So what is the correct answer?

This problem and its variations fall into word problems that provide many unrelated details to the question.

They are all unsolvable.

When I said it’s a simple math problem you can’t solve, that was not a challenge. It was a statement of fact.

The Shunqing Education Department posted a statement saying the test had intended to “examine… critical awareness and an ability to think independently”.

The implications!

We seem to emphasize goal orientation more than critical thinking in our education and experiences.

The presence of unrelated facts doesn’t always craftily lead to an answer.

Think of our own life experiences.

How often do we listen to a media story with many exciting facts and assume they logically lead to a conclusion? They don’t always!

Ever react to a friend’s passing comment about a headache with a recommendation for a specific painkiller?

I have often seen it in business, where information is abundant but irrelevant to the question. 

No matter the number of goats or sheep on the boat, you don’t have enough information to determine the Captain’s age.

Sometimes we just need the right information.

Finally, it’s worth remembering that everything in life is not a problem to be solved.

What do you think? Leave me a comment below.