T 55 - Let be a star, not a starlet.

In the text T 53 of your review « Les Héritiers d'Archimède » which is on your site, I read the question: How to build 6 rows of 4 trees if you have only 12 trees. I think, that here, I give the answer !

In this country, every integer is a A-star, generally called a star. Of course, we have many stars.

A B-star is a star of 12 stars so that every row of 4 stars gives us the same sum (6 times for every star). These 12 numbers can be consecutive.

A primitive B-star is a B-star, the sum of each of its row is minimum. The schema in this text gives you such a star.

A C-star is composed of 12 B-stars. And the sum of the 16 A-stars in each of its 12 rows of 4 B-stars is the same. Of course.

Is it possible to create a star-arithmetic. I think so.

Take a B-star and add each of its 12 summits the same number; you obtain a A-star; Well!
Take two B-stars. Add summit by summit these two B-stars; you obtain a B-star; Very-well!
Take a B-star and multiply each of its 12 summits by the same number; You obtain...Well!

The operations on stars and numbers are not difficult indead.

I shall try to explain you one of the simplest way to construct a C-star.


First I chose one B-star (those on the top of the scheme that I can call the root-star or the root). And I shall multiply it, twelve times by a number. Which numbers? Not difficult to find. Look.

My root will give me the top of the C-star. I have multiply the root by 1
The B-star where I have number 2 will be the root star multiply by 2,
The B-star where I have number 3 will be the root star multiply by 3,

The B-star where I have number 12 will be the top star multiply by 12.

And, it's ended.

Who shall send to ADCS the first D-star (use our mail) ? He will receive a book (the french translation of « Martin's Gardner Sixth book of Mathematical Games from Scientific American » autographed by the author of this text. And, necessary, your production will give us a new text.

Let be a star.

Your friend Ulysse Servo