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(*OUEST -> SUD*) ((0b1111 land t) lsl 8) + (*EST -> NORD*) lor ((0b11110000 land t) lsl 8) + (*SUD -> EST*) lor ((0b111100000000 land t) lsr 4) + (*NORD -> OUEST*) lor ((0b1111000000000000 land t) lsr 12) + +let n = 6 +let m = 4 + +let is_placeable (b : board) (i : int) (j : int) (t : tuile) : bool = + (**cette fonction travaille sur un tore + on a pas trouvé de solutions dans ce cadre*) + ( (*NORD*) + ( + (b.(i).((j-1+m) mod m) <> -1) + && (((b.(i).((j-1+m) mod m) land 0b0000011100000000) lsr 8 ) = ((t land 0b0111000000000000) lsr 12)) + (*&& (((b.(i).((j-1+m) mod m) lxor t ) land 0b0000100000000000) = 0b1000000000000000)*) + ) || (b.(i).((j-1+m) mod m) = -1) + ) + && + ( (*SUD*) + ( + (b.(i).((j+1+m) mod m) <> -1) + && (((b.(i).((j+1+m) mod m) land 0b0111000000000000) lsr 12) = ((t land 0b0000011100000000) lsr 8)) + (*&& (((b.(i).((j+1+m) mod m) lxor t ) land 0b1000000000000000) = 0b0000100000000000)*) + ) || (b.(i).((j+1+m) mod m) = -1) + ) + && + ( (*EST*) + ( + (b.((i+1+n) mod n).(j) <> -1) + && (((b.((i+1+n) mod n).(j) land 0b0000000000000111) lsr 0 ) = ((t land 0b0000000001110000) lsr 4)) + (*&& (((b.((i+1+n) mod n).(j) lxor t ) land 0b0000000000001000) = 0b0000000010000000)*) + ) || (b.((i+1+n) mod n).(j) = -1) + ) + && + ( (*OUEST*) + ( + (b.(((i-1+n) mod n)).(j) <> -1) + && (((b.(((i-1+n) mod n)).(j) land 0b0000000001110000) lsr 4 ) = ((t land 0b0000000000000111) lsr 0)) + (*&& (((b.(((i-1+n) mod n)).(j) lxor t ) land 0b0000000010000000) = 0b0000000000001000)*) + ) || (b.(((i-1+n) mod n)).(j) = -1) + ) + +let is_placeable_non_tore (b : board) (i : int) (j : int) (t : tuile) : bool = + (**Ne travaille pas sur un tore. avec les points, il devrait y avoir 2 solutions.*) + ( (*NORD*) + if (j <> 0) then + ( + (b.(i).(j-1) <> -1) + (*la première ligne fait la couleur, la seconde les points.*) + && (((b.(i).(j-1) land 0b0000011100000000) lsr 8 ) = ((t land 0b0111000000000000) lsr 12)) + && (((b.(i).(j-1) land 0b0000100000000000) lsr 8 ) <>((t land 0b1000000000000000) lsr 12)) + ) || (b.(i).(j-1) = -1) + else true + ) + && + ( (*SUD*) + if j <> m-1 then + ( + (b.(i).(j+1) <> -1) + && (((b.(i).(j+1) land 0b0111000000000000) lsr 12) = ((t land 0b0000011100000000) lsr 8)) + && (((b.(i).(j+1) land 0b1000000000000000) lsr 12) <>((t land 0b0000100000000000) lsr 8)) + ) || (b.(i).(j+1) = -1) + else true + ) + && + ( (*EST*) + if i <> n-1 then + ( + (b.(i+1).(j) <> -1) + && (((b.(i+1).(j) land 0b0000000000000111) lsr 0 ) = ((t land 0b0000000001110000) lsr 4)) + && (((b.(i+1).(j) land 0b0000000000001000) lsr 0 ) <>((t land 0b0000000010000000) lsr 4)) + ) || (b.(i+1).(j) = -1) + else true + ) + && + ( (*OUEST*) + if i <> 0 then + ( + (b.(i-1).(j) <> -1) + && (((b.(i-1).(j) land 0b0000000001110000) lsr 4 ) = ((t land 0b0000000000000111) lsr 0)) + && (((b.(i-1).(j) land 0b0000000010000000) lsr 4 ) <>((t land 0b0000000000001000) lsr 0)) + ) || (b.(i-1).(j) = -1) + else true + ) + + +let soltuion_nb = ref 0 + +let incr_sol_nb () : unit = + soltuion_nb := !soltuion_nb + 1; + (*au début je pensait compter toutes les solutions + c'est un peut long.*) + (if !soltuion_nb mod 1000000000 = 0 then begin + Printf.printf " found %d billion solutions \n" (!soltuion_nb/1000000000); + flush stdout + end) + +let print_board (b : board) : unit = + Printf.printf " FOUND A SOLUTION : \n"; + for j = 0 to m-1 do + for i = 0 to n-1 do + Printf.printf " %x " (b.(i).(j) (*land 0b0111011101110111*) ) + done; + print_newline() + done + +let rec find_soltution (b : board) (pieces : tuile list) (i : int) (j : int) : unit = + if pieces = [] || (j = m) then begin + print_board b; + incr_sol_nb () + end + else + (*print_board b;*) + let possibles = List.map (fun t -> t, + [t; + t |> rotate_left; + t |> rotate_left |> rotate_left; + t |> rotate_left |> rotate_left|> rotate_left] + ) pieces in + (*List.iter (fun (t,l) -> List.iter (fun t_placed -> + Printf.printf " %x - " t_placed + )l; + Printf.printf "\n" + ) possibles;*) + List.iter (fun (t,l) -> + List.iter (fun t_placed -> + if is_placeable_non_tore b i j t_placed then begin + b.(i).(j) <- t_placed; + find_soltution b + (List.filter (fun p -> p <> t) pieces) + ((i+1) mod n) + (if i+1 = n then (j+1) else j) + end else () + ) l + ) possibles + +let _ = + let b = Array.make_matrix n m (-1) in + find_soltution b [ + (*BLANC : 01 ROUGE : 11 BLEU : 10*) + (*dans l'ordre alphabétique*) + 0b1011_1001_1001_0001; + 0b1010_1001_0001_0001; + 0b1010_1011_1011_0011; + 0b0001_0010_1011_1010; + 0b1010_0001_0011_0011; + 0b0010_1010_1010_1010; + 0b0011_1001_1001_0011; + 0b1010_1001_1001_0010; + 0b0010_0011_0011_0010; + 0b1011_1010_1001_0010; + 0b0011_1001_1010_1010; + 0b1011_0011_0011_1011; + 0b0011_1011_1001_1011; + 0b0010_0010_0001_0010; + 0b0010_0010_1011_1010; + 0b0010_1011_1001_1011; + 0b1001_1001_1001_0001; + 0b1001_0010_0001_0011; + 0b1001_0001_1011_1011; + 0b0001_0001_1010_1010; + 0b0011_1011_1010_0010; + 0b1001_0011_1010_1011; + 0b0001_0001_0011_0010; + 0b0001_0011_1001_0010 + ] + 0 0; + Printf.printf "there are about %d solutions total !\n" (!soltuion_nb) + diff --git a/RapportsEtonnements/2024-ThuillierAubert.md b/RapportsEtonnements/2024-ThuillierAubert.md new file mode 100644 index 00000000..d7b1f48c --- /dev/null +++ b/RapportsEtonnements/2024-ThuillierAubert.md @@ -0,0 +1,62 @@ +### `Châteaux magiques | Des Automates` + +#### Principe : + +On donne au élèves un plan de Château, sur lequel le passage d'une pièce à l'autre se fait par un mot magique. Et on leur demande de répondre à des questions sur l'automate. + +#### Exemples de questions posées : + +- trouver un chemin de longueur paire (impossible) +- Trouver le chemin le plus long +- Donner des conditions d'accessibilité + +#### Observations sur la séance : + +1. Les groupes n’allaient pas tous à la même vitesse et pouvaient être complètement bloqués par certaines questions +2. Sur l’institutionnalisation, il a fallu qu’on se reprenne dans nos premières explications. +3. faire des meilleurs plans de châteaux (encore plus clairs, cf. les étages qui sont assez difficile à lire, même si en pratique ça n’a pas dérangé les groupes les plus efficaces) +4. Retravailler la formulation des questions et éventuellement en changer l’ordre + +### `Puzzle de Mac-Mahon | Puzzle Np-complet` + +#### Principe : + +On donne au élèves 24 pièces de puzzle, et ils doivent le résoudre. On leur demande aussi un peu plus tard de trouver une méthode générale pour essayer de résoudre de façon automatisée le puzzle. + +#### Observation et suggestions d’amélioration : + +1. Ils ont eu du mal avec le concept d'algorithme et décrire une méthode algorithmique de résolution ; L’idéal serait de trouver une autre activité connexe aux puzzles de Mac-Mahon pour qu’ils ne passent pas l’heure entière à résoudre le puzzle +2. Lorsqu’on a demandé aux élèves de chercher une méthode générale, la plupart des groupes ont simplement continué de chercher une solution au puzzle. + +### `Blasons | Grammaires,encodage, langages de programmation` + +#### Principe : + +On donne au élèves des images de blasons. L'un d'eux pioche un blason sans le montrer et le décrit au autres, qui doivent le dessiner. + +#### Observations et suggestions d’amélioration : + +1. Les élèves se sont pris au jeu, même si certains étaient très tentés de décrire avec des mouvements, ce qui faisait perdre l’intérêt du jeu +2. On a pu mettre en évidence la notion d’ambiguïté de la grammaire en faisant un exemple avec un élève au tableau +3. Mettre les blasons dans un format un peu plus grand et opaque (par exemple en carton) pour éviter que les dessinateurs ne puissent voir le blason à travers la feuille +4. Ce serait bien de pouvoir proposer une activité d’approfondissement un peu plus précise, par exemple décrire un jeu de dérivations de mots pour construire des formules et ainsi décrire les rudiments d’une grammaire hors contexte + +### `Puzzle Humains | calcul en parallèle` + +#### Principe : + +On donne au élèves des grandes cartes qui représentent un puzzle +et ils doivent le résoudre, soit tous ensemble de façon désordonnée, soit avec un seul directeur d’opérations qui décide qui fait quoi, soit avec tout le monde suivant des instructions précises. + +#### Observations et suggestions d’amélioration :  + +1. On s’est vite rendu compte que le format de puzzle humain n’était pas pratique. On a alors décidé de remplacer le puzzle par des listes de nombres. +2. On a constitué deux groupes. Dans les deux cas, on a appliqué des algorithmes de tri selon les configurations décrites dans la section principe. Activité faite à l'extérieur +3. Dans l’un des deux groupes, on a eu le temps de présenter le tri fusion et de le faire appliquer la partie fusion à un élève directeur d'opérations en plus +4. Utiliser des listes (au moins au début) plutôt que des puzzles +5. Faire des plus petit groupes pour les tris de listes par un seul directeur d’opérations (des listes de 6 à 10 personnes seraient idéal) + +### `Contribution personnelle : Puzzle de Mac-Mahon (PuzzleMathematique)` + +Construction de l’activité dans le cadre de l’ENS Rennes (inspiré de , cf. jour 16 sur la page) +Réalisations : Les puzzles, un programme en OCaml pour trouver une solution (pour pouvoir la présenter au élèves et leur prouver que ce n'était pas impossible), institutionnalisation + trace écrite + fiche de préparation \ No newline at end of file