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Joute n°184 : Pi Day +14
Bonjour à tous,
J'ai découvert avec effroi que j'avais raté le Pi Day 
.
Pour les autres étourdis comme moi, c'était le 14 mars à 9h26 (mais les opinions divergent sur l'heure exacte Bon anniversaire de Pi).
Pour me rattraper, voici une petite joute utilisant les décimales de 
, que m'a proposée littleguy (merci à lui 
).
Les quarante-cinq premières décimales de sont :
141592653589793238462643383279502884197169399
Si on les regroupe par trois, on obtient les quinze nombres suivants :
141-592-653-589-793-238-462-643-383-279-502-884-197-169-399
Parmi ceux-ci, quatre seulement sont premiers : 653, 643, 383 et 197.
Question : Comment ranger toutes ces décimales de sorte qu'en les regroupant par trois, on obtienne quinze nombres premiers tous distincts (ne commençant pas par 0), et que ce nouvel ordre donne un nombre de 45 chiffres le plus petit possible ?
Bonjour
c'est déjà dur d'en trouver 15...
Je donne:
101 113 223 227 233 389 449 463 569 599 647 659 859 887 983
Et tant , je réponds quand même ....
101-113-223-227-233-347-449-499-569-599-659-683-859-863-887
Merci pour l'énigme !!
Bonjour Godefroy,
Pour le minimum:
101-113-223-227-233-347-389-449-499-569-659-683-859-887-233-
Pour le maximum (non demandé)
997-991-983-977-883-881-661-659-653-541-523-443-409-223-883-
Merci pour la joute
Bonjour à tous.
Je propose la suite :
101, 113, 223, 227, 233, 347, 449, 499, 569, 599, 659, 683, 859, 863, 887.
Merci pour l'énigme.
RE
Vu le nombre de réponses,et pour l'honneur
Je donne le plus petit:
101 113 223 227 233 389 449 463 569 599 647 659 859 887 983
PARDON
j'ai redonné le même (plusieurs clones)
il faut prendre 349 en 6ème position au lieu de 389
101 113 223 227 233 349 449 499 569 659 683 853 859 887 967
Merci pour le poisson Godefroy,
Et zut!
Un erreur idiote d'affichage le dernier nombre est fautif!
101-113-223-227-233-347-389-449-499-569-659-683-859-887-569- pour le minimum
Bonjour godefroy,
On range les décimales comme suit :
101113223227233347449499569599659683859863887
La suite des nombres premiers obtenus est alors
[101, 113, 223, 227, 233, 347, 449, 499, 569, 599, 659, 683, 859, 863, 887]
Merci pour cette énigme difficile !
Clôture de l'énigme :
Pas beaucoup de réponses cette fois-ci. 
Il faut dire qu'elle est moins facile qu'elle n'en avait l'air.
Merci encore à littleguy !
Félicitations à Nofutur2 pour sa première victoire (de l'année). 
Bravo également à masab et blumaise ! 
Bravo à Nofutur2.
La solution pour le max est
997-991-983-977-883-881-661-659-643-541-523-503-443-229-223-
J'ai corrigé mes erreurs de programmation.
CONST PI = "141592653589793238462643383279502884197169399"
CONST NB_PRI = 143
CONST NB_NIV = 15
CONST Faux = (0 = 1)
CONST Vrai = NOT (Faux)
DATA 101,103,107,109,113,127,131,137,139,149
DATA 151,157,163,167,173,179,181,191,193,197
DATA 199,211,223,227,229,233,239,241,251,257
DATA 263,269,271,277,281,283,293,307,311,313
DATA 317,331,337,347,349,353,359,367,373,379
DATA 383,389,397,401,409,419,421,431,433,439
DATA 443,449,457,461,463,467,479,487,491,499
DATA 503,509,521,523,541,547,557,563,569,571
DATA 577,587,593,599,601,607,613,617,619,631
DATA 641,643,647,653,659,661,673,677,683,691
DATA 701,709,719,727,733,739,743,751,757,761
DATA 769,773,787,797,809,811,821,823,827,829
DATA 839,853,857,859,863,877,881,883,887,907
DATA 911,919,929,937,941,947,953,967,971,977
DATA 983,991,997
' compter les repetitions des chiffres de pi.
TYPE stPrime
n AS STRING * 3
r AS STRING * 10
END TYPE
DIM SHARED ch(9) AS INTEGER, prime(NB_PRI) AS stPrime, Lim AS STRING * 10, way AS STRING * 10, nbSol AS LONG
CALL Init_0
CALL Traiter
END
FUNCTION MayAdd% (p AS INTEGER)
SHARED Lim AS STRING * 10, way AS STRING * 10, prime() AS stPrime
DIM rep AS INTEGER, x AS INTEGER, y AS INTEGER, z AS INTEGER, t AS INTEGER, w AS STRING * 10
DIM a AS STRING * 3
CALL Pause
a = prime(p).n
w = way
rep = Vrai
FOR i = 1 TO 3
t = ASC(MID$(a, i, 1)) - 48
x = 1 + ASC(MID$(w, t + 1, 1)) - 48
y = ASC(MID$(Lim, t + 1, 1)) - 48
IF x > y THEN
rep = Faux
EXIT FOR
ELSE
MID$(w, t + 1, 1) = CHR$(x + 48)
END IF
NEXT i
IF rep THEN
way = w
END IF
MayAdd% = rep
END FUNCTION
SUB See (n1 AS INTEGER, n2 AS INTEGER, n3 AS INTEGER, n4 AS INTEGER, n5 AS INTEGER, n6 AS INTEGER, n7 AS INTEGER, n8 AS INTEGER, n9 AS INTEGER, n10 AS INTEGER, n11 AS INTEGER, n12 AS INTEGER, n13 AS INTEGER, n14 AS INTEGER, n15 AS INTEGER)
SHARED Lim AS STRING * 10, way AS STRING * 10, prime() AS stPrime, nbSol AS LONG
DIM rep AS STRING
rep = STR$(nbSol) + ":"
rep = rep + prime(n1).n + "-"
rep = rep + prime(n2).n + "-"
rep = rep + prime(n3).n + "-"
rep = rep + prime(n4).n + "-"
rep = rep + prime(n5).n + "-"
rep = rep + prime(n6).n + "-"
rep = rep + prime(n7).n + "-"
rep = rep + prime(n8).n + "-"
rep = rep + prime(n9).n + "-"
rep = rep + prime(n10).n + "-"
rep = rep + prime(n11).n + "-"
rep = rep + prime(n12).n + "-"
rep = rep + prime(n13).n + "-"
rep = rep + prime(n14).n + "-"
rep = rep + prime(n15).n + "-"
LOCATE 20, 1: PRINT rep
PRINT #1, rep
PRINT way
PRINT Lim
END SUB
SUB Traiter
SHARED way AS STRING * 10, nbSol AS LONG
DIM i1 AS INTEGER, i2 AS INTEGER, i3 AS INTEGER
DIM i4 AS INTEGER, i5 AS INTEGER, i6 AS INTEGER
DIM i7 AS INTEGER, i8 AS INTEGER, i9 AS INTEGER
DIM i10 AS INTEGER, i11 AS INTEGER, i12 AS INTEGER
DIM i13 AS INTEGER, i14 AS INTEGER, i15 AS INTEGER
DIM Push_way(NB_NIV) AS STRING * 10
OPEN "C:\_ile\184.sol" FOR OUTPUT AS #1
nbSol = 0
way = STRING$(10, "0")
FOR i1 = 1 TO NB_PRI - 14
LOCATE 1, 1: PRINT USING "### \ \ "; i1; prime(i1).n
Push_way(1) = way
IF MayAdd%(i1) THEN
FOR i2 = i1 + 1 TO NB_PRI - 13
LOCATE 2, 1: PRINT USING "### \ \"; i2; prime(i2).n
Push_way(2) = way
IF MayAdd%(i2) THEN
FOR i3 = i2 + 1 TO NB_PRI - 12
LOCATE 3, 1: PRINT USING "### \ \"; i3; prime(i3).n
Push_way(3) = way
IF MayAdd%(i3) THEN
FOR i4 = i3 + 1 TO NB_PRI - 11
LOCATE 4, 1: PRINT USING "### \ \"; i4; prime(i4).n
Push_way(4) = way
IF MayAdd%(i4) THEN
FOR i5 = i4 + 1 TO NB_PRI - 10
LOCATE 5, 1: PRINT USING "### \ \"; i5; prime(i5).n
Push_way(5) = way
IF MayAdd%(i5) THEN
FOR i6 = i5 + 1 TO NB_PRI - 9
LOCATE 6, 1: PRINT USING "### \ \"; i6; prime(i6).n
Push_way(6) = way
IF MayAdd%(i6) THEN
FOR i7 = i6 + 1 TO NB_PRI - 8
LOCATE 7, 1: PRINT USING "### \ \"; i7; prime(i7).n
Push_way(7) = way
IF MayAdd%(i7) THEN
FOR i8 = i7 + 1 TO NB_PRI - 7
LOCATE 8, 1: PRINT USING "### \ \"; i8; prime(i8).n
Push_way(8) = way
IF MayAdd%(i8) THEN
FOR i9 = i8 + 1 TO NB_PRI - 6
LOCATE 9, 1: PRINT USING "### \ \"; i9; prime(i9).n
Push_way(9) = way
IF MayAdd%(i9) THEN
FOR i10 = i9 + 1 TO NB_PRI - 5
LOCATE 10, 1: PRINT USING "### \ \ "; i10; prime(i10).n
Push_way(10) = way
IF MayAdd%(i10) THEN
FOR i11 = i10 + 1 TO NB_PRI - 4
Push_way(11) = way
IF MayAdd%(i11) THEN
FOR i12 = i11 + 1 TO NB_PRI - 3
Push_way(12) = way
IF MayAdd%(i12) THEN
FOR i13 = i12 + 1 TO NB_PRI - 2
Push_way(13) = way
IF MayAdd%(i13) THEN
FOR i14 = i13 + 1 TO NB_PRI - 1
Push_way(14) = way
IF MayAdd%(i14) THEN
FOR i15 = i14 + 1 TO NB_PRI
Push_way(15) = way
IF MayAdd%(i15) THEN
nbSol = nbSol + 1
PRINT nbSol; ":"
CALL See(i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12, i13, i14, i15)
END
END IF 'IF MayAdd%(i15) THEN
way = Push_way(15)
NEXT i15
way = Push_way(14)
END IF 'IF MayAdd%(i14) THEN
NEXT i14
way = Push_way(13)
END IF 'IF MayAdd%(i13) THEN
NEXT i13
way = Push_way(12)
END IF 'IF MayAdd%(i12) THEN
NEXT i12
way = Push_way(11)
END IF 'IF MayAdd%(i11) THEN
NEXT i11
way = Push_way(10)
END IF 'IF MayAdd%(i10) THEN
NEXT i10
way = Push_way(9)
END IF 'IF MayAdd%(i9) THEN
NEXT i9
way = Push_way(8)
END IF 'IF MayAdd%(i8) THEN
NEXT i8
way = Push_way(7)
END IF 'IF MayAdd%(i7) THEN
NEXT i7
way = Push_way(6)
END IF 'IF MayAdd%(i6) THEN
NEXT i6
way = Push_way(5)
END IF 'IF MayAdd%(i5) THEN
NEXT i5
way = Push_way(4)
END IF 'IF MayAdd%(i4) THEN
NEXT i4
way = Push_way(3)
END IF ' IF MayAdd%(i3) THEN
NEXT i3
way = Push_way(2)
END IF ' IF MayAdd%(i2) THEN
NEXT i2
way = Push_way(1)
END IF ' IF MayAdd%(prime(i1).n) THEN
NEXT i1
CLOSE #1
END SUB
SUB Init_0
SHARED ch() AS INTEGER, prime() AS stPrime, Lim AS STRING * 10
DIM i AS INTEGER, j AS INTEGER, k AS INTEGER, a AS STRING * 3, b AS STRING * 10, x AS INTEGER
CALL Init
FOR i = 0 TO 9: ch(i) = 0: NEXT i
FOR i = 1 TO LEN(PI): x = VAL(MID$(PI, i, 1)): ch(x) = ch(x) + 1: NEXT i
Lim = STRING$(10, "0"): FOR i = 0 TO 9: MID$(Lim, i + 1, 1) = CHR$(48 + ch(i)): NEXT i
FOR i = 0 TO 9: PRINT i; " "; ch(i): NEXT i: PRINT Lim
RESTORE
FOR i = 1 TO NB_PRI
READ a
'j = i:
j = NB_PRI + 1 - i
prime(j).n = a
prime(j).r = STRING$(10, "0")
FOR k = 1 TO 3
'ex 479
'position 4+1 =5
'0000000000
'0000*00000
' 0+1=1
'0000100000
x = ASC(MID$(a, k, 1)) - 48
y = ASC(MID$(prime(j).r, x + 1, 1)) - 48 + 1
MID$(prime(j).r, x + 1, 1) = CHR$(y + 48)
NEXT k
'PRINT i; " "; prime(i).n; " "; prime(i).r
NEXT i
END SUB
SUB Init
SCREEN 0: WIDTH 150, 45: _FONT 16
CLS
END SUB
FUNCTION Maxy (p1, p2)
IF p1 > p2 THEN
Maxy = p1
ELSE
Maxy = p2
END IF
END FUNCTION
FUNCTION Miny (p1, p2)
IF p1 < p2 THEN
Miny = p1
ELSE
Miny = p2
END IF
END FUNCTION
SUB Pause
y$ = INKEY$
IF LEN(y$) > 0 THEN
END
END IF
END SUB
FUNCTION NoSpace$ (p AS STRING)
NoSpace$ = LTRIM$(RTRIM$(p))
END FUNCTION
FUNCTION Net$ (p AS LONG, p1 AS LONG)
Net$ = RIGHT$(SPACE$(p1) + STR$(p), p1)
END FUNCTION
FUNCTION ToStr$ (p AS LONG)
ToStr$ = LTRIM$(STR$(p))
END FUNCTION
FUNCTION inArray% (p1 AS LONG, p2() AS LONG)
DIM i AS LONG, ret AS INTEGER
ret = Faux
FOR i = 1 TO p2(0)
IF p2(i) = p1 THEN
ret = Vrai
EXIT FOR
END IF
NEXT i
inArray% = ret
END FUNCTION
FUNCTION Pgcd& (p1 AS LONG, p2 AS LONG)
DIM a AS LONG, b AS LONG, q AS LONG, r AS LONG
a = Maxy(p1, p2)
b = Miny(p1, p2)
r = a MOD b
DO WHILE NOT (r = 0)
a = b
b = r
r = a MOD b
LOOP
Pgcd& = b
END FUNCTION
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