Tuesday, January 15, 2013

Grille de la semaine #13

Aujourd'hui, une variante du fameux Masyu. Le Mystery Masyu voit apparaître deux nouveaux types de cercles :
- les cercles gris sont "neutres" ; à leur contact, la boucle se comporte comme si elle atteignait un cercle blanc ou un cercle noir.
- les cercles bicolores sont également neutres, mais les deux cercles d'une même paire, correspondant à deux cercles symétriques par rapport au centre de la grille, sont affectés d'une relation antagoniste ; si l'un est blanc, l'autre sera noir et vice-versa.

Règles :
Dessinez une boucle fermée passant d'une case à l'autre horizontalement ou verticalement. La boucle doit passer par toutes les cases contenant un cercle.
Lorsqu'elle atteint un cercle noir, la boucle doit immédiatement effectuer un quart de tour puis traverser la case suivante.
Lorsqu'elle atteint un cercle blanc, la boucle doit le traverser en ligne droite puis effectuer immédiatement un quart de tour en atteignant la case voisine (d'un côté de la case au cercle blanc au minimum).
Les cercles bicolores sont antagonistes ; deux cercles bicolores symétriques par rapport au centre de la grille sont nécessairement de couleur différente.
Draw a closed loop passing horizontally or vertically through neighbouring cells. The loop must go through every cell containing a circle.
When reaching a black circle, the loop must immediately make a right-angled turn, then pass straight through the next cell.
When reaching a white circle, the loop must immediately pass straight through, then make a right-angled turn when reaching the next cell (on at least one side of the white circle cell).
Bicolor circles are antagonistic; two bicolor circles which are symmetrical with regard to the center of the grid are necessarily of different colors.

#15 Mystery Masyu



  1. I seem to be getting multiple solutions for this. Basically I get a forced single solution IF R4C3 behaves horizontally, but if it does vertically (http://prasannaseshadri.files.wordpress.com/2013/01/image-58.png), it has many ways in the top left. Am I missing something?

    The curious thing is, I think it'd have a unique solution if all grey circles were turned into bicolor? The bicolor is a nice idea btw, and I liked the solve until the last bit.

  2. Of course you are right, the puzzle has way too many solutions. The issue comes from the fact that I designed it on paper and used a very similar notation for both types of circles, hence the confusion when re-drawing it. Actually, only one pair of grey circles would need to be turned to bicolor (admitting I am not missing anything, this time) but it would leave only one pair of grey circles in the grid and switching them to bicolor doesn't really affect the difficulty of the puzzle; so, radical decision: no more grey circles. Simpler rules, better aesthetics... and a puzzle far from being minimal, but I can probably live with it.

    Thanks a lot for the comment; I promise tomorrow's sudoku will have been carefully checked!