How old is the captain? Everyone knows these insoluble problems which end with this famous question. Here’s a fun version that has a very simple solution.
You probably know the expression “the age of the captain. It generally designates a mathematical problem with an absurd statement containing no information allowing an answer to the question asked. We owe its origin to Gustave Flaubert who had submitted to his sister, who is keen on geometry, a little insoluble riddle, to tease her: he talked about a ship, giving lots of useless details that had no connection with each other (cargo, number of passengers, wind direction, time, etc.). ) For ask him to deduce the captain’s age, which was obviously impossible.
Since then, the question has been declined in countless forms, often very funny, to make fun of the absurdity of certain mathematical problems, like the famous stories about faucets and bathtubs which have traumatized generations of schoolchildren and which have entered the collective imagination. However, it is entirely possible to build on this model a puzzle that is apparently insoluble, but which is solved very easily, as in the following example. Will you be able to solve it? Take the test before reading the solution below. Here is the statement.
On the Castafiore’s birthday, Tintin tells Captain Haddock.
“By the way, Captain, in five years you will be exactly twice the age I am today.
– It’s normal, cabin boy: you are twenty years younger than me!”
How old is the captain?
Contrary to appearances, this little problem is very simple to solve. All you have to do is ask yourself the right question and rephrase the information given in the statement.
What are we looking for? Captain Haddock’s age today. Let’s call it C for writing convenience (it’s shorter than “the captain’s age”, math people are lazy!). Even if this is not the primary objective, it is also a question of Tintin’s age, which we do not know any further. Let’s call it T. Note that we can do without this second unknown, by limiting ourselves to doing everything with C, provided we are comfortable.
That said, let’s “translate” the information distilled in the statement. In fact, there are only two, but it is enough to determine the two unknowns, T and C. It is said that in five years, the age of the captain (so C + 5) will be double of that of Tintin today (so 2 x T or, more simply, 2T) which amounts to writing C + 5 = 2T. We also know that Tintin is twenty years younger than the captain, i.e. T = C – 20.
We can then rephrase the first sentence as follows: C + 5 = 2(C-20). In other words, a banal equation with a single unknown (C) that simply needs to be simplified with classic calculation rules, while maintaining the balance of equality, like on a scale: C + 5 = 2C – 40either 5 + 40 = 2C – Chence C = 45. Captain Haddock is therefore 45 years old, and Tintin 25, which is consistent with Hergé’s characters whose age has never changed throughout their adventures.
This example – which I imagined for my students when I was a math teacher – illustrates simple principles that go beyond the scope of math. First, you must always ask yourself what you are looking for: this seems obvious, but many people get lost from the start by having the wrong goal. Then, that math is above all a language – calculations are accessory tools. It was enough to translate the sentences written in French into this symbolic language for the apparently complex statement to become simple and clear. Certainly, this is not the case with more complex concepts based on very abstract notions, but, in everyday life, this simple “translation” is enough to deal with many problems.