{"id":1219,"date":"2023-04-03T09:29:53","date_gmt":"2023-04-03T08:29:53","guid":{"rendered":"https:\/\/blog.univ-angers.fr\/mathsinfo\/?page_id=1219"},"modified":"2023-04-05T10:02:48","modified_gmt":"2023-04-05T09:02:48","slug":"challenges-2023-pour-calculatrices-hp","status":"publish","type":"page","link":"https:\/\/blog.univ-angers.fr\/mathsinfo\/challenges-2023-pour-calculatrices-hp\/","title":{"rendered":"Challenges 2023 pour calculatrices HP"},"content":{"rendered":"\n

Voici les challenges que j’ai propos\u00e9s sur Twitter et Facebook (HP Calculator Fan Club<\/a>), \u00e0 programmer sur calculatrices HP. <\/p>\n\n\n\n

Je mets des solutions en RPL (pour HP 48-49-50 g) et parfois pour d’autres machines (HP 12C, HP 35S, HP Prime…). J’ajoute des solutions en Python et APL.<\/p>\n\n\n\n

Enonc\u00e9s et corrig\u00e9s<\/h2>\n\n\n
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CHALLENGE #1<\/h3>\n\n\n\n
=== HP 48+ - Eric Schraf ===\n\n\u00ab 0 + \u2192t \t\t' t = {0, numbers...}\n\u00ab 0 1 9 FOR i\t        ' m = 0 ; for i = 1 to 9\n  t i - NOT\t\t' t == i ? -> {True False...}\n  \u03a3LIST\t\t\t' n = sum({True False...})\n  DUP 2 > * i *\t\t' p = n * i * (n > 2)\n  MAX NEXT \u00bb \u00bb\t        ' m = max(p, m)\n'CH01 STO\n\n1: {4 4 4 9 9 9}\nVAR CH01\n1: 27\n\n=== Version Python - Eric Schraf ===\n\ndef ch01(arr):\n  maxi = 0\n  for v in set(arr): \n    n = arr.count(v)\n    if n > 2: maxi = max(maxi, n * v)\n  return maxi\n\n>> ch01([4,4,4,9,9,9])\n27\n>> ch01([1,1,9,9,2,1,2,2,1])\n6\n\n=== Version APL - Eric Schraf ===\n\n      \u2308\/, {\u237a \u00d7 (n > 2) \u00d7 n \u2190 \u2374\u2375} \u2338 4 4 4 4 9 9 9\n27\n      \u2308\/, {\u237a \u00d7 (n > 2) \u00d7 n \u2190 \u2374\u2375} \u2338 1 1 9 9 2 1 2 2 1\n6<\/code><\/pre>\n\n\n
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CHALLENGE #2<\/h3>\n\n\n\n
=== HP 48+ - Eric Schraf ===\n\n\u00ab {} SWAP WHILE DUP 0 >   ' Transformation nombre en liste\nREPEAT DUP 10 MOD ROT +   ' Ajout de l'unit\u00e9 \u00e0 la liste\nSWAP 10 \/ IP END          ' On passe \u00e0 l'unit\u00e9 suivante\nDROP \u0394LIST                ' Diff\u00e9rences successives\nABS 1 >                   ' Test si certains d\u00e9passent 1\n\u03a3LIST NOT                 ' On les compte : 1 si aucun > 1\n\u00bb\n'CH02 STO\n\n1: 5654\nVAR CH02\n1: 1\n1: 798\nCH02\n1: 0\n\n=== HP Prime - Uwe Sauerland ===\n\nEXPORT ch02(n)\nBEGIN\n  LOCAL k, s := STRING(n);\n  FOR k FROM 1 TO DIM(s) - 1 DO\n    IF ABS(EXPR(s[k, 1]) - EXPR(s[k + 1, 1])) \u2260 1 THEN\n      RETURN 0;\n    END;\n  END;\n  RETURN 1;\nEND;\n\n=== Version APL - Eric Schraf ===\n\n      ch02 \u2190 \u2227\/ 1 = \u2218 | 2 -\/ (\u234e\u00a8 \u2355)\n\n      ch02 '5654'\n1\n      ch02 '798'\n0\n      ch02 '12345654565432123'\n1<\/code><\/pre>\n\n\n
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CHALLENGE #3<\/h3>\n\n\n\n
=== HP48+ - Eric Schraf ===\n\n\u00ab \"123456789\" \u2192 t s          ' t = longueur voulue\n\u00ab s t 1 FOR j                ' for j = t to 1 step -1\nj RAND * CEIL DUP 'K' STO    ' k = randint(1, j+1) \nDUP SUB 'V' STO              ' Echanger s[k] et s[j]\ns K s j j SUB REPL           \nj V REPL\nDUP 's' STO -1 STEP          ' next \nt SUB OBJ\u2192                   ' transformation chaine en nombre\n\u00bb \u00bb<\/code><\/pre>\n\n\n\n
=== HP PRIME - Eric Schraf ===\n\nch03:= X \u2192 EXPR(cat(randperm(X)))\n\nch03(5) --> 52143\nch03(1) --> 1\n\n=== APL - Eric Schraf ===\n\n      ch03 \u2190 10 \u22a5 ?\u2368\n\n      ch03 5\n23415\n      ch03 1\n1\n      ch03 9\n165493278<\/code><\/pre>\n\n\n
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CHALLENGE #4<\/h3>\n\n\n\n
Voici le code <\/a>t<\/a>r<\/a>o<\/a>u<\/a>v<\/a>\u00e9<\/a> <\/a>s<\/a>u<\/a>r<\/a> <\/a>r<\/a>o<\/a>s<\/a>e<\/a>t<\/a>t<\/a>a<\/a>c<\/a>o<\/a>d<\/a>e<\/a>.<\/a>o<\/a>r<\/a>g<\/a> <\/a>que j’ai traduit<\/a> :<\/p>\n\n\n\n
=== HP48+ - Eric Schraf === (code IS-BASIC sur rosetta.org)\n\n\u00ab \u2192 n\n\u00ab 1 n FOR i\n  1 n FOR j\n  2 i * DUP j - n + 1 - n MOD n *\n  SWAP j + 2 - n MOD + 1 +\n  NEXT NEXT\n  N DUP 2 \u2192LIST \u2192ARRY\n\u00bb \u00bb<\/code><\/pre>\n\n\n
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Carr\u00e9 magique 5×5<\/figcaption><\/figure>\n<\/div>\n\n
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Version de @david_cobac<\/a><\/figcaption><\/figure>\n<\/div>\n\n
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CHALLENGE #5<\/h3>\n\n\n\n
Chaque minute, la grande aiguille avance de 6\u00b0 et la petite de 0,5\u00b0 (car 30\u00b0 en 60 minutes)
HH.MM correspond \u00e0 60 * HH + MM minutes. La grande aiguille sera \u00e0 l’angle 360 * HH + 6 * MM et la petite aiguille en 30 * HH + 0,5 * MM. L’angle entre les 2 = 330 * HH + 5,5 * MM<\/p>\n\n\n\n
=== HP48+ - Eric Schraf ===\n\n\u00ab DUP FP 550 *\n  SWAP IP 330 * + 360 MOD \u00bb\n\nou encore :\n\n\u00ab DUP FP 580 *\n  SWAP 30 * - 360 MOD \u00bb\n\n=== HP 35S, 33S... - Werner Huysegoms ===\n\n00 { 26-Byte Prgm }\n01\u25b8LBL \"H.M\u2221\"\n02 ENTER\n03 FP\n04 580\n05 \u00d7\n06 X<>Y\n07 30\n08 \u00d7\n09 -\n10 360\n11 MOD\n12 END\n\n=== Version Python - Eric Schraf ===\n\ndef ch05(hmm):\n  return round((580 * (hmm % 1) - 30 * hmm) % 360, 2)\n\n>> ch05(3.00)\n270.0\n>> ch05(4.34)\n67.0\n>> ch05(2.15)\n22.5\n\n=== Version APL n\u00b01 - Eric Schraf ===\n\n      ch05 \u2190 360 | (580 \u00d7 1 | \u22a2) - 30 \u00d7 \u22a2\n\n      ch05\u00a8 3 4.34 6 2.15\n270 67 180 22.5\n\n=== Version APL n\u00b02 - Eric Schraf ===\n\n      ch05 \u2190 360 | 580 30 -.\u00d7 (1 | \u22a2), \u22a2\n\n      ch05\u00a8 3 4.34 6 2.15\n270 67 180 22.5<\/code><\/pre>\n\n\n
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CHALLENGE #6<\/h3>\n\n\n\n
Pour les calculatrices ayant la fonction DDAYS<\/strong> (nombre de jours entre 2 dates), il suffisait de compter le nombre de jours entre la date voulue et un dimanche quelconque<\/span>, par exemple le 2\/2\/3000 (date tr\u00e8s \u00e9loign\u00e9e dans le futur !). Ensuite on regarde le reste de la division de ce nombre de jours par 7.<\/p>\n\n\n\n
=== HP48+ - Joseph Horn ===\n\n\u00ab 2.023 SWAP DDAYS 7 MOD \u00bb\n\n=== HP12C ===\n\n01-36\t\tENTER\n02-02\t\t2\n03-00\t\t0\n04-02\t\t2\n05-03\t\t3\t\t'A changer chaque ann\u00e9e\n06-26\t\tEEX\n07-06\t\t6\n08-16\t\tCHS\n09-40\t\t+\n10-02\t\t2\n11-48\t\t.\n12-00\t\t0\n13-02\t\t2\n14-03\t\t3\n15-43.26\tg DYS\n16-07\t\t7\n17-10\t\t\/\n18-43.24\tg FRAC\n19-01\t\t1\n20-30\t\t-\n21-07\t\t7\n22-20\t\t\u00d7\n23-16\t\tCHS\n24-31\t\tR\/S\n25-43.33.01\tg GTO 01<\/code><\/pre>\n\n\n\n
Si maintenant votre calculatrice n’a pas la fonction DDAYS<\/strong>, vous pouvez utiliser la formule g\u00e9n\u00e9rale : jour_sem = jour + code(mois) + an + [an \/ 4] – 2<\/strong> pour les ann\u00e9es de la forme 20an. Je vous conseille ma vid\u00e9o Youtube<\/a> \u00e0 ce sujet. <\/p>\n\n\n\n
Les codes des mois sont \u00ab\u00a0144025036146\u00a0\u00bb<\/p>\n\n\n\n
Ann\u00e9e 2023<\/span> (an = 23) : an + [an \/ 4] – 2 = 23 + [23 \/ 4] – 2 = 26 = 5<\/strong> modulo 7. 
On ajoute donc +5 aux codes des mois ce qui donne \u00ab\u00a0622503514624\u00a0\u00bb (toujours modulo 7).<\/p>\n\n\n\n
Ann\u00e9e 2024<\/span> (an = 24) : an + [an \/ 4] – 2 = 24 + [24 \/ 4] – 2 = 28 = 0<\/strong> modulo 7. 
Mais attention, 2024 est une ann\u00e9e bissextile, plus pr\u00e9cis\u00e9ment elle l’est \u00e0 partir du 1er mars, avant on ne voit pas la diff\u00e9rence avec une ann\u00e9e \u00ab\u00a0normale\u00a0\u00bb. Il faut donc enlever 1 pour janvier et f\u00e9vrier, ce qui donne le code \u00ab\u00a0034025036146\u00a0\u00bb<\/p>\n\n\n\n
=== HP48+ (Pour l'ann\u00e9e 2023) - Eric Schraf ===\n\n\u00ab DUP FP 2 ALOG * SWAP IP DUP\n\"622503514624\" UNROT SUB\nOBJ\u2192 + 7 MOD \u00bb\n\n=== HP48+ (Pour l'ann\u00e9e 2024) - Eric Schraf ===\n\n\u00ab DUP FP 2 ALOG * SWAP IP DUP\n\"034025036146\" UNROT SUB\nOBJ\u2192 + 7 MOD \u00bb\n\n=== HP 33S, 35S... - Eric Schraf ===\n\n00001  ENTER\n00002  FP\n00003  100\n00004  \u00d7\n00005  x<>y\n00006  IP\n00007  +\/-\n00008  10^x\n00009  426415305226   (pour 2023)\n00010  \u00d7\n00011  FP\n00012  10\n00013  \u00d7\n00014  IP\n00015  +\n00016  7\n00017  RMDR\n\n=== APL - Eric Schraf ===\n\n      ch06 \u2190 {7 | (100 \u00d7 1|\u2375) + \u234e '622503514624'[\u230a\u2375]}\n\n      ch06\u00a8 12.31 4.04 10.27\n0 2 5<\/code><\/pre>\n\n\n
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CHALLENGE #7<\/h3>\n\n\n\n
V<\/td>60<\/td><\/tr>
D<\/td>30.4<\/td><\/tr>
D1<\/td>10.4<\/td><\/tr>
D2<\/td>40.5<\/td><\/tr><\/tbody><\/table>
Exemple de donn\u00e9es initiales : On veut 60L d’un liquide \u00e0 30,4\u00b0C en m\u00e9langeant des liquides \u00e0 10,4\u00b0C et 40,5\u00b0C.<\/figcaption><\/figure>\n\n\n
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Formules permettant de d\u00e9terminer les volumes respectifs \u00e0 utiliser.<\/figcaption><\/figure>\n<\/div>\n\n\n
=== HP 42S, 41C... - Werner Huysegoms ===\n\n00 { 16-Byte Prgm }\n01\u25b8LBL \"IPOL\"\n02 STO- ST Z\n03 -\n04 \u00f7\n05 \u00d7\n06 STO- ST Y\n07 X<>Y\n08 END\n\n=== HP Prime - Uwe Sauerland ===\n\nEXPORT ch07(p1, p2, p3, m)\nBEGIN\n  LOCAL m1 := (p3 - p2) \/ (p1 - p2);\n  RETURN m * { m1, 1 - m1 };\nEND;\n\n=== HP 33S, 35S - Eric Schraf ===\n\nPas     Code (42 octets)\n00001   FN = F\n00002   SOLVE X\n00003   V-X\n00004   STOP\nF0001   LBL F\nF0002   SF 11\nF0003   V\u00d7(D-B)\u00f7(A-B)=X\nF0004   RTN\n\n=== Autre version pour HP 33S, 35S - Eric Schraf ===\n'On cherche l'\u00e9quation de la droite passant par (0, D1) et (V, D2)\n'puis l'abscisse qui donnera D en ordonn\u00e9e\n'Visuel ci-dessous\n\nPas     Code (36 o)\n00001   CL\u03a3\n00002   R\u2191\n00003   \u03a3+\n00004   LASTx\n00005   R\u2193\n00006   CLx\n00007   \u03a3+\n00008   R\u2193\n00009   R\u2193\n00010   x\u0302\n00011   -\n00012   LASTx<\/code><\/pre>\n\n\n
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Challenge #8<\/h3>\n\n\n\n
=== HP 41C + compatible - Werner Huysegoms ===\n\nGTO \"CH8\", then 6 R\/S 18 R\/S etc\n\n00 { 23-Byte Prgm }\n01\u25b8LBL \"CH8\"\n02 0\n03\u25b8LBL 10      @ M-m m\n04 STOP        @ X M-m m\n05 RCL ST Z\n06 -           @ X-m M-m m\n07 X>Y?\n08 X<>Y\n09 X>0?\n10 CLX\n11 STO+ ST Z\n12 -\n13 GTO 10\n14 END\n\n=== HP48g+ - Werner Huysegoms ===\n\nCH8: \u00ab DUP LMAX SWAP LMIN - \u00bb\nLMAX: \u00ab 0 \u00ab OVER MAX \u00bb FLIST \u00bb\nLMIN: \u00ab DUP HEAD \u00ab OVER MIN \u00bb FLIST \u00bb\nFLIST: \u00ab ROT 1 ROT DOSUBS SWAP DROP \u00bb<\/code><\/pre>\n\n\n
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=== HP48g+ - Eric Schraf ===\n\nSCA: \u00ab \u2192 v f \u00ab v \u00ab OVER f EVAL \u00bb STREAM v SIZE \u2192LIST \u00bb\nCH8: \u00ab DUP \u00ab MAX \u00bb SCA SWAP \u00ab MIN \u00bb SCA - \u00bb<\/code><\/pre>\n\n\n\n
=== APL - Eric Schraf ===\n\n      ch08 \u2190 \u2308\\ - \u230a\\\n\n      ch08 6 18 \u00af2 100 23 \u00af30\n0 12 20 102 102 130<\/code><\/pre>\n\n\n
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Challenge #9<\/h3>\n\n\n\n
Le calcul math\u00e9matique du temps d’attente du premier arriv\u00e9 au rendez-vous n’est pas simple ! Par contre, par simulation, on obtient facilement une estimation du r\u00e9sultat. En effet, il suffit pour chaque exp\u00e9rience de tirer 2 nombres entiers entre 0 et 59 et de regarder leur diff\u00e9rence en valeur absolue (qui est donc le temps d’attente du premier arriv\u00e9). On recommence l’exp\u00e9rience des centaines ou milliers de fois et on constate qu’en moyenne le temps sera de 20 minutes<\/strong>.<\/p>\n\n\n\n
=== HP 42S - Werner Huysegoms ===\n\n00 { 43-Byte Prgm }\n01\u25b8LBL \"CH09\"\n02 STO \"N\"\n03 STO \"M\"\n04 0\n05\u25b8LBL 10\n06 XEQ 14\n07 XEQ 14\n08 -\n09 ABS\n10 +\n11 DSE \"M\"\n12 GTO 10\n13 RCL\u00f7 \"N\"\n14 RTN\n15\u25b8LBL 14\n16 RAN\n17 60\n18 \u00d7\n19 IP\n20 END\n\n=== HP 48+ - Werner Huysegoms ===\n\n\u00ab \u2192 N \u00ab\n0 1 N START\nR59 R59 - ABS + NEXT\nN \/ \u00bb \u00bb\n\n'R59':\n\u00ab RAND 60 * IP \u00bb\n\n=== HP Prime - Uwe Sauerland ===\n\nEXPORT ch09(samples)\nBEGIN\n LOCAL k, totalWT := 0;\n FOR k FROM 1 TO samples DO\n  LOCAL sample := ABS(deltalist(RANDINT(2, 0, 59)));\n  totalWT := totalWT + sample(1);\n END;\n return totalWT \/ samples;\nEND;\n<\/code><\/pre>\n\n\n
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=== Version APL ===\n\n      ch09 \u2190 { \u2375 \u00f7\u2368 +\/ | - \u233f ? 2 \u2375 \u237460 }\n\n      ch09 100\n18.94\n      ch09 10000\n20.0471\n      ch09 100000\n20.04593\n      ch09 1000000\n19.996039<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
Voici les challenges que j’ai propos\u00e9s sur Twitter et Facebook (HP Calculator Fan Club), \u00e0 programmer sur calculatrices HP. Je mets des solutions en RPL (pour HP 48-49-50 g) et parfois pour d’autres machines (HP 12C, HP 35S, HP Prime…). … Continuer la lecture →<\/span><\/a><\/p>\n","protected":false},"author":4913,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1219","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/pages\/1219","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/users\/4913"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/comments?post=1219"}],"version-history":[{"count":73,"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/pages\/1219\/revisions"}],"predecessor-version":[{"id":1315,"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/pages\/1219\/revisions\/1315"}],"wp:attachment":[{"href":"https:\/\/blog.univ-angers.fr\/mathsinfo\/wp-json\/wp\/v2\/media?parent=1219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}