Numbered houses

The workings

As those who have come across set theory at some point know, counting is nothing more than a particular way of establishing a bijection between some set and a special set, such as the natural numbers. This simple idea, though perhaps a bit far-fetched in expression, is the first way in which human beings related to the concepts of number or quantity, using pebbles instead of words, or even notches on a bone. The image in the entry – in which the bones of Lebombo and Ishango can be seen – belongs to the latter type. Although the latter is much better known, the former is the earliest known to be used for what purpose.

Getting back to words, and without going into linguistic theories (which some people have already got into with mathematical and systematic eagerness), the story of the creation of numbers reminds me of a beautiful sentence from the beginning of One Hundred Years of Solitude, with which we will end:

Many years later, as he faced the firing squad, Colonel Aureliano Buendía was to remember that distant afternoon when his father took him to discover ice. At that time Macondo was a village of twenty adobe houses, built on the bank of a river of clear water that ran along a bed of polished stones, which were white and enormous, like prehistoric eggs. The world was so recent that many things lacked names, and in order to indicate them it was necessary to point.

The fun

The conversation between two mathematicians exchanging home addresses goes as follows:

–What is the number of your house?

–In my street the houses are numbered consecutively, from number one onwards. It turns out that the numbers of the houses on one side of mine add up to the same number as the numbers of the houses on the other side. What a coincidence!

–I can’t determine the number with that information -the other quickly replies-. Tell me at least how many houses there are, right?

–I can’t remember how many there are. I counted them a long time ago. I don’t know… between two and three hundred.

Is it possible to determine the number of the house?

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Solution

We encourage the readers to try to solve the divertimento for themselves. Whether you succeed or not, you can always consult the solution in this link.