# The Josephus Problem

## "What one fool can do, another can."

This chapter of Concrete Mathematics is trickier than the previous ones. I drew many images and found the pattern myself but had to turn to the book for advice on how to formalize it.

And… **Anti-Congrats** to myself for bumping into the first derivation I'm not
getting 😕 . Or rather it should be called a **gap** in the derivation. I noticed
that mathematicians like those **gaps** *so much*. As a programmer 👩💻 , I'm used
to writing down the instructions precisely, one by one, without omitting any
steps required for the successful execution of a task at hand. It's different
with mathematicians. They like to skip steps. (IMO, **one of** the rare exceptions
to this tendency is the book Discrete Mathematics with
Applications written by **Susanna S. Epp**.)

Supposedly, it means the authors expect their readers should be able to grasp
the **gaps** left. Or the authors don't notice there are any **gaps** at all. Or
what if they do it on purpose, to set a high bar for people trying to understand
the topic? This might make sense. The fewer people **get** mathematics, the more
mathematicians are in deficit; with the consequence that math professionals are
in greater demand and self-perceived value. Well, I really don't know. I'm still
figuring out the answer to this question ^{1}.

So now I'm going to take a break, probably for a day or two. Such breaks often help to "digest" a task to solve, so I hope the next time I delve into this topic again I'll be able to fully understand the derivation and fill in the gaps.

## Footnotes:

^{1}

Appears I am not alone in my perception. The following is
the quote from the — still popular! — book Calculus Made
Easy by **S. P. Thompson**, first published back in `1910`

:

Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks.

Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics — and they are mostly clever fools — seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way.

Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.