1. Confettis log(n) (solution)

L’astuce consiste simplement à plier la feuille plusieurs fois puis de perforer. A chaque perforation, il sort autant de confetti que le nombre de plis. Il n’est pas possible de plier indéfiniment, la feuille devient vite difficile à percer. Il y a un compromis à trouver.

../_images/confetti2.png ../_images/confetti3.png

Mais alors pourquoi confettis log(n) ?

Lorsqu’on plie une fois la feuille, chaque perforation produit deux confettis. On va deux fois plus vite. Si on plie deux fois la feuille, il y a quatre épaisseurs. On va quatre fois plus vite. Si on plie trois fois, il y a huit épaisseurs. On va huit fois plus vite.

Et si on raisonne à l’envers. En dix secondes, une personne a fait 10 confettis et une autre 80. Il y a 8 fois plus de confettis. Combien de fois a-t-elle plié sa feuille ? La réponse est

System Message: WARNING/2 (3 = \ln_2 8)

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System Message: WARNING/2 (\ln_2(x))

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est le logarithme en base 2 de x.

1.1. A quoi ça sert ?

Pour découper deux formes identiques, le plus simple est de les découper en même temps. Elles sont identiques aux imperfections près.