Cinquante signes

Oui, pourquoi ? D’abord les mélodies, ensuite un certain dandysme bienvenu des Frenchies. Mais c’est la faute aussi à  Laure Adler, laquelle eut le génie de les retenir au  générique de son « Heure bleue », émission que les  couche-tard connaissent bien — et générique dont  nous allons causer maintenant. Le morceau s’appelle « Veridis Quo », il date de 2001 et se joue sur les quatre notes d’un synthé japonais à deux balles. Le beat minimaliste et entêtant vous prend  par sa mélancolie : oui, nous avons raté nos vies, mais  nous nous déhancherons quand même encore un petit  peu, si vous le permettez. Une autre vertu du couple Thomas Bangalter et Guy- Manuel de Homem-Christo est son souci de la typo et des jeux de langue en général. Alors, en fouillant, on tombe sur ça — et on se pâme (à deux balles aussi) : "Veridis quo" is a wordplay on the Latin phrase "Quo vadis?" literally, "Whither goest thou?" or "Where are you going?" The greater meaning of...

  Hello math-Fun, The chess fairy piece « Imitator » is a gem that has led to beautiful problems for more than 80 years now (have a look here ). Could it be possible to build an integer sequence based on a similar idea? Our Imitator is here a small black spot placed under the first digit of the sequence S. We've decided that the Imitator must always slide from under an odd digit to under another odd digit of S. The Imitator will be driven right or left by the successive terms of S. When a(n) is odd, the Imitator moves under a(n) digits to the right. When a(n) is even, the Imitator moves under a(n) digits to the left. That’s it (for the Imitator). We want as usual S to be the lexicographically earliest sequence of distinct positive integers with this property. If I’m not wrong, S starts like this: S = 1, 3, 5, 2, 7, 4, 6, 9, 11, 10, 13, 15, 8, 12, 17, 19, 21,… Let’s check the behavior of the Imitator (the small black i under a digit of S). (if needed, click ...

This is the common typeface used hereunder for each of the 10 digits Today, we want to produce a sequence S of integers a(n) where a(n) is the cumulative sum of the matches used so far in S . S starts with 4 as 4 is the smallest available integer that uses 4 matches ( S must be the lexicographically earliest sequence of distinct terms with this property). It follows: S = 4, 7, 11, 19, 27. S is impossible to extend after a(5) = 27. Let's try to go further with a different start: T = 5, 12, 17. End. Backtracking for another start with a(1) = 5: T = 5, 12, 22, 32. End. Another start: U = 6, 13, 23, 33, 42, 52, 63. End. Well... But our imagination is without limits! We had the hereunder (stupid and horrible) idea – which was to extend the above lexico-first S with a(6) = 42, like this: S  = 4, 7, 11, 19, 27. (45-3), ...  (45 - 3 = 42) Yes, I know, Goya was right, El sueño de la razon produce monstruos ... ... this technique allows us to go further, and, probably, to extend ...

Hello Math-Fun, Say every integer > 9 can produce an h x w rectangle (height first, then width). We would then have: 10 = 1 x 0 (no rectangle, nothing that we will use here) 11 = 1 x 1 (the unit cell) 12 = 1 x 2 (see below) 13 = 1 x 3 (see below) ... 21 = 2 x 1 (see below) 31 = 3 x 1 (see below) ... 100 = 10 x 0 (no rectangle, nothing that we will use here) 101 = 10 x 1 (no other choice, we don't accept any height or width  starting with zero) ... 111 = 1 x 11 or 11 x 1 112 = 1 x 12 or 11 x 2 ... 2023 = 20 x 23 or 202 x 3 ... We will use "NR" for the integers of the above left column (NR stands for N umber- R ectangle) Now we want two things: 1) to tile an n x n square with distinct shapes of NRs 2) the sum of the NRs involved in the tiling is itself a square.   Examples +---+ |   | the 11-NR +---+ +---+---+ |   |   | the 12-NR +---+---+ +---+---+---+ |   |   |   | the 13...