2ãåºãšããäºé²å¯Ÿæ°log_{2}(x)ãlb(x)ã§è¡šããšãlb(3),lb(5),lb(7),lb(11),lb(13)ã®é£åæ°å±éã¯ã
lb(3)=[1;1,1,2,2,3,1,5,2,23,...]
lb(5)=[2;3,9,2,2,4,6,2,1,1,3,1,18..]
lb(7)=[2;1,4,5,4,5,4,1,29,...]
lb(11)=[3;2,5,1,1,1,25,1,1,...]
lb(13)=[3;1,2,2,1,22,23,1,9,149,...]
ã§ãlb(13)ã[3;1,2,2,1,22,23,1,9]ã§è¿äŒŒãããšã
[3;1,2,2,1,22,23,1,9]-lb(13)=201130/54353-lb(13)
=-2.25897731584196266637728075571*10^-12
ãšãªã£ãŠã201130/54353ãlb(13)ã®è¿äŒŒå€ãšãããšèª€å·®ãå°ããã®ã§ãlb(3),lb(5),lb(7),lb(11)ã
54353åãããšã
54353*lb(3)=86147.4668016970019305550728204
54353*lb(5)=126203.757741412805693795471951
54353*lb(7)=152588.162078596956051793358299
54353*lb(11)=188030.486767793017766203979679
ãšãªã£ãŠãå°æ°éšåã«çç®ãããšã
0.4668016970019305550728204=[0;2,7,33,...]
0.757741412805693795471951=[0;1,3,7,...]
0.162078596956051793358299=[0;6,5,1,...]
0.486767793017766203979679=[0;2,18,2,...]
ãªã®ã§ããããããã1/2=[0;2],3/4=[0;1,3],1/6={0;6],1/2=[0;2]ã§è¿äŒŒãããšã
(86147+1/2)/54353-lb(3)=6.10790627896702020627740913203*10^-7
(126203+3/4)/54353-lb(5)=-1.42428436437616975547826382828*10^-7
(152588+1/6)/54353-lb(7)=8.44124466103963591405650940218*10^-8
(188030+1/2)/54353-lb(11)=2.43449432087167148461376935139*10^-7
ãšãªããŸããã(86147+1/2)/54353,(126203+3/4)/54353,(152588+1/6)/54353,(188030+1/2)/54353ãé£åæ°å±éãããšã
(86147+1/2)/54353=[1;1,1,2,2,3,1,5,2,2,1,2,1,12]
(126203+3/4)/54353=[2;3,9,2,2,4,4,1,1,6,1,1,2]
(152588+1/6)/54353=[2;1,4,5,4,5,5,1,4,1,1,2,3]
(188030+1/2)/54353=[3;2,5,1,1,1,25,1,4,1,1,4,2]
ããã
lb(3)ã§[1;1,1,2,2,3,1,5,2,...]ã
lb(5)ã§[2;3,9,2,2,4,...]ã
lb(7)ã§[2;1,4,5,4,5,...]ã
lb(11)ã§[3;2,5,1,1,1,25,1,...]
ãŸã§äžèŽããŠããŠãlb(3),lb(5),lb(7),lb(11),lb(13)ã忝ã54353*12=652236ã®åæ°ã§æ¯èŒçããè¿äŒŒã§ãããã§ãã
No.2210kuiperbelt2024幎9æ30æ¥ 20:09
lb(3),lb(5),lb(7),lb(11),lb(13)ãéåžžã«é£åæ°ããã®æã¡åãåæ°ã§
忝ã6æ¡ã§ãããã®ããšããš
lb(3)=301994/190537
lb(5)=227268/97879ã(6æ¡ã§ãããã®ã¯åããªãã£ãã)
lb(7)=1273419/453601
lb(11)=1444074/417431
lb(13)=201130/54353
ãèŠã€ããã
kuiperbeltæ°ã«ããæ§æã§ã¯
lb(3)=172295/108706=1033770/652236
lb(5)=504815/217412=1514445/652236
lb(7)=915529/326118=1831058/652236
lb(11)=376061/108706=2256366/652236
lb(13)=201130/54353=2413560/652236
ããã§åãã®æ¹ã®ç°ãªãåæ°ã652236ãžãšçµ±äžãããšããã°ããããã®ååã¯
lb(3)-->round(652236/190537*301994)=1033770
lb(5)-->round(652236/97879*227268)=1514445
lb(7)-->round(652236/453601*1273419)=1831058
lb(11)-->round(652236/417431*1444074)=2256366
lb(13)-->round(652236/54353*201130)=2413560
ãšççŸãªãã€ãªãããŸããã
No.2211GAI2024幎10æ1æ¥ 08:46
ããããããã®ãä»äºã§
ããã ãã®çŽ æ°ã«å¯Ÿããåžžçšå¯Ÿæ°å€ãå
±é忝ã§
log2 = 360565/1197771 = 0.3010299966 (çå€ 0.3010299957)
log3 = 571482/1197771 = 0.4771212527 (çå€ 0.4771212547)
log5 = 837206/1197771 = 0.6989700034 (çå€ 0.6989700043)
log7 = 1012234/1197771 = 0.8450981031 (çå€ 0.8450980400)
log11 = 1247350/1197771 = 1.0413927203 (çå€ 1.0413926852)
log13 = 1334249/1197771 = 1.1139433164 (çå€ 1.1139433523)
log17 = 1473796/1197771 = 1.2304488922 (çå€ 1.2304489214)
log19 = 1531654/1197771 = 1.2787536182 (çå€ 1.2787536010)
log23 = 1631038/1197771 = 1.3617277426 (çå€ 1.3617278360)
log29 = 1751618/1197771 = 1.4623980711 (çå€ 1.4623979979)
忝ã®1197771ã¯10000000ãŸã§ã§æã誀差ãå°ãªããªãå€ã§ãã
ã®æ§ã«æ§æå¯èœã§ããããšã«é©ããŸãããããµãšåæ¯ãæããªããšã
忝ã¯ãã®ã«ãã£ãŠå€åãããŠããããªãã©ããªãã®ãæ°ã«ãªã£ãŠèª¿ã¹ãŠã¿ãŸããã
3æ¡ã»ã©ã®åæ°ã§ã®è¿äŒŒã¯ã忝ãæããããšã«æããªããªã
gp > abs(146/485-log(2)/log(10))
%469 = 9.3217107035117801368259509460209827810 E-7
gp > abs(73/153-log(3)/log(10))
%470 = 2.9282868735104173903973984794620415878 E-6
gp > abs(339/485-log(5)/log(10))
%471 = 9.3217107035117801368259509460209517576 E-7
gp > abs(431/510-log(7)/log(10))
%472 = 7.9857055620241233702400874249978544429 E-10
gp > abs(478/459-log(11)/log(10))
%473 = 1.6503537575300559002466218995055742675 E-6
gp > abs(743/667-log(13)/log(10))
%474 = 3.2382107964776722479812223847580763836 E-7
gp > abs(299/243-log(17)/log(10))
%475 = 3.7535188454130236161139021156448952272 E-6
gp > abs(656/513-log(19)/log(10))
%476 = 1.1643056554722575810391097558286690920 E-6
gp > abs(1103/810-log(23)/log(10))
%477 = 5.5904413551619395128281053884536869710 E-7
gp > abs(525/359-log(29)/log(10))
%478 = 2.4547234686221517882671475279717504814 E-6
ã®æ§ãªåæ°ã§ããªãã®ç²ŸåºŠãäžããããã§ãã
No.2179GAI2024幎9æ18æ¥ 08:34
è¿äŒŒåæ°ã«é¢ããŠã¯ä»¥åå°ãç ç©¶ããããšããããŸãã
ïŒåæ°ã®æé ã§ç²ŸåºŠé ã«åæ°ãåæããæ¹æ³ãèããŸãã(äœåæ¡ã§ãOK)ãïŒ
æžãããŠããåæ°ã¯ããã¹ãŠé£åæ°ãæã¡åã£ãŠåŸãããåæ°ã§ããã
ãããããã¯ã3æ¡ä»¥äžã§æãè¯ããåæ°ãåŸããããšã¯éããŸããã
äŸãã°log17ã¯299/243ãã881/716ã®æ¹ãè¯ãè¿äŒŒã«ãªããŸãã
åæ§ã«log29ã525/359ãã914/625ã®æ¹ãå°ãã ãè¯ãè¿äŒŒã«ãªããŸãã
log23ã¯3æ¡ä»¥äžã§é£åæ°æã¡åãã§åŸãããåæ°ã§ã¯64/47ãæå€§ã§
粟床ãåºãªãããã«åå4æ¡ã蚱容ãããã®ãšæããŸããã
975/716ã§ãããããã®ç²ŸåºŠã¯åºãŸãã
倧åã®å€ã¯ãå°æ°ç¹ä»¥äžã®ç²ŸåºŠã(åæ¯ã®æ¡æ°Ã2)æ¡çšåºŠã«ãªããŸããã
ããŸããŸé£åæ°æã¡åãçŽåŸã®å€ã倧ããå Žåã¯ç²ŸåºŠãè¯ããªããŸããã
log7ã¯[0;1,5,2,5,6,1,4813,1,1,âŠ]ã§4813ã®åã§æã¡åã£ãŠãããã
ããã ãç¹å¥ã«ç²ŸåºŠãè¯ããªã£ãŠããŸãã
ååšçã®355/113ãåæ§ã§ããã
No.2180ãããã2024幎9æ18æ¥ 10:24
åã« 1 ã€ã®å¯Ÿæ°å€ãæ©æ¢°èšç®ãèš±ããŠèªç±ã«æçæ°è¿äŒŒããã ãã§ãããã
æ°åŠæåç§è©± > 环ä¹ã®äž 4 æ¡
ä»ããã®ãµã€ãã®äœã¶æãã§åãè°è«ãç¹°ãè¿ãè¡ãããŠããŸããã
No.2181DD++2024幎9æ18æ¥ 21:45
29ãŸã§ã®çŽ æ°ã§ãåžžçšå¯Ÿæ°ã®é£åæ°å±éãæ±ããŠã¿ãŸããããlog_{10}(7)ã®ãšãã®4813ã®ãããªå€§ããªæ°ã¯çŸããŸããã§ããããªããlog_{10}(5)=1-log_{10}(2)ãªã®ã§çç¥ããŠããŸãã
log_{10}(2)=[0;3,3,9,2,2,4,6,2,1,1,3,1,18,...]
[0;3,3,9,2,2,4,6,2,1,1,3,1]=97879/325147
=0.301029995663499893894146339963
log_{10}(3)=[0,2,10,2,2,1,13,1,7,18,...]
[0,2,10,2,2,1,13,1,7]=34367/33001
=0.477121254550546065527863343601
log_{10}(11)=[1;24,6,3,2,1,1,3,1,1,1,9,...]
[1;24,6,3,2,1,1,3,1,1,1]=22014/21139
=1.04139268507014938941244204721
log_{10}(13)=[1;1,8,1,3,2,7,1,6,16,...]
[1;1,8,1,3,2,7,1,6]=5113/4590
=1.11394335511982570806100217865
log_{10}(17)=[1,4,2,1,17,1,13,1,1,3,3,26,...]
[1;4,2,1,17,1,13,1,1,3,3]=99797/81106
=1.23045150790323773826843883313
log_{10}(19)=[1;3,1,1,2,2,1,3,2,2,1,4,1,1,1,6,1,3,1,3,1,47,...]
[1;3,1,1,2,2,1,3,2,2,1,4,1,1,1,6,1,3,1,3,1]=6497723/5081294
=1.27875360095282815755199364571
log_{10}(23)=[1;2,1,3,4,17,2,1,2,66,...]
[1;2,1,3,4,17,2,1,2]=9016/6621
=1.36172783567436943059960731007
log_{10}(29)=[[1;2,6,6,1,2,1,2,2,2,1,1,1,1,1,5,1,2,3,37,...]
[1;2,6,6,1,2,1,2,2,2,1,1,1,1,1,5,1,2,3]=5243915/3585833
=1.46239799789895402267757589380
No.2188kuiperbelt2024幎9æ22æ¥ 14:46
log[10]7ã§é£åæ°ã®8çªç®ã®å€ã4813ã§ããã
log[10]2ã¯137çªç®ã5393
log[10]3ã¯562çªç®ã2788
log[10]11ã¯2179çªç®ã3864
log[10]13ã¯133çªç®ã1378
log[10]17ã¯710çªç®ã3301
log[10]19ã¯1341çªç®ã2249
log[10]23ã¯921çªç®ã2695
log[10]29ã¯352çªç®ã1901
ã®ããã«ãã£ãšå
ãŸã§èŠãã°å€§ããªæ°ã¯ãããåºãŠããŸãã
log[10]7ã¯å¥è·¡çã«åã®æ¹ã«ãã£ããšããããšã§ããã
No.2189ãããã2024幎9æ22æ¥ 15:53
å
æ¥ãç§ã¯ãµãš 4374 ãš 4375 ãã©ã¡ãã 1 æ¡ã®çŽ å æ°ããæããªãããšã«æ°ã¥ããŸããã
ãããŠã224 ãš 225ã2400 ãš 2401 ãåæ§ã®æ§è³ªãæã€ãšç¥ã£ãŠããç§ã¯ã以äžã®ãããªèšç®ãåŸãŸããã
log ã¯å
šãŠåžžçšå¯Ÿæ°ã§ãã
224 â 225 ãã
5 log 2 + log 7 â 2 log 3 + 2 log 5
2400 â 2401 ãã
5 log 2 + log 3 + 2 log 5 â 4 log 7
4374 â 4375 ãã
log 2 + 7 log 3 â 4 log 5 + log 7
ãããŠã
log 2 + log 5 = 1
ããããé£ç«ã㊠4 å
1 次æ¹çšåŒãšæã£ãŠè§£ããšãå°æ°ç¬¬6äœåæšäºå
¥ã§
log 2 â 72/239 â 0.30126 ïŒçå€ 0.30103ïŒ
log 3 â 114/239 â 0.47699 ïŒçå€ 0.47712ïŒ
log 5 â 167/239 â 0.69874 ïŒçå€ 0.69897ïŒ
log 7 â 202/239 â 0.84519 ïŒçå€ 0.84510ïŒ
ããããŠæ¯èŒçç°¡åã«ããè¿äŒŒå€ãåŸãããããã§ãã
ãããèŠãŠçåãããã€ãã
(1)
忝 239 ãšããã®ã¯ã©ã®ãããã®åªç§ããªãã§ããããïŒ
ããªãã¡ã4 ã€ã®å¯Ÿæ°ã忝ãå
±éãªæçæ°ã§è¿äŒŒããå Žåã忝<1000 ãããã§äœçªç®ãããã«åªç§ãªè¿äŒŒå€ãåŸããã忝ãªãã§ããããïŒ
ïŒçµ¶å¯Ÿèª€å·®ã®åã§è©äŸ¡ãããçžå¯Ÿèª€å·®ã®åã§è©äŸ¡ãããã§ãå€ãããšæããŸããïŒ
(2)
4 æ¡ã§å·®ã 1 ã§ãããã®ãããã7æ¡ä»¥äžã§å·®ã 11 ã 13 ãããã¯ããããå«ã 2 æ¡ãããã®åææ°ã§ãããã®ãçšããæ¹ã粟床ããããªããããªæ°ãããŸãâŠâŠæ¬åœã§ããããïŒ
æ¬åœã ãšããŠãå
·äœçã«ã©ã®ããã粟床ãäžããããã§ãããïŒ
ïŒå·®ã 1 æ¡ã®çŽ å æ°ããæããªããã®ã¯ãABCäºæ³ã®èšŒæãä¿¡ãããªã 44100 ããå
ã«ã¯ååšããªãã¯ãïŒ
(3)
â ã§ã¯ãªããäžçå·ã§ã®è©äŸ¡ã¯åæ§ã®æ¹æ³ã§å¯èœã§ããããïŒ
(4)
䜿ãçŽ æ°ã« 11 ãå«ã㊠5 å
1 次ã«ããã䜿ãçŽ æ°ã« 13 ãŸã§å«ã㊠6 å
1 次ã«ããããªã©ã§ç²ŸåºŠã®åäžã¯å¯èœã§ããããïŒ
ç¹ã« (1) (2) (4) ã¯æäœæ¥ã§ã¯ç¡è¬ã«ãã»ã©ãããã®ã§ãã³ã³ãã¥ãŒã¿ç³»ã®æŽè»ããé¡ãããŸãã
No.2156DD++2024幎9æ15æ¥ 10:30
ãšãããã(1)ã ã
> 忝 239 ãšããã®ã¯ã©ã®ãããã®åªç§ããªãã§ããããïŒ
忝ïŒ1000ã§ã¯(çžå¯Ÿèª€å·®ã®åèšã§)70çªç®ã«åªç§ã§ããã
239ã§çžå¯Ÿèª€å·®ã®åèšã¯0.001457âŠã§ãã
1äœã¯568ã§ãçžå¯Ÿèª€å·®ã®åèšã¯0.0001758âŠã§ãã
2äœä»¥äžã¯897,960,807,794,âŠãšç¶ããŸããã忝ã倧ãããã°çžå¯Ÿèª€å·®ãå°ããã®ã¯åœç¶ã§ã
ããããæå³ã§ã¯69çªç®ãŸã§ã«åæ¯ã239æªæºã®ãã®ã¯ãããŸããã®ã§ã239ã¯çµæ§åªç§ãšèšãããšæããŸãã
忝ã®å€§ãããèæ
®ããŠãçžå¯Ÿèª€å·®ã®åèšÃ忝ãã§ã©ã³ãã³ã°ãäœããšã
1äœã®568ã2äœã®897ã¯å€ãããŸãããã3äœã329ããããŠ4äœã239ãšãªããŸãã
çžå¯Ÿèª€å·®ã®åèšÃ忝ã®å
·äœå€(5äœãŸã§)ã¯
568 0.099882607730
897 0.222871229356
329 0.285662258393
239 0.348293385746
103 0.383956736568
ã®ããã«ãªã£ãŠããŠããããèŠãŠã568ã ãçªåºããŠããæãã§ãã
ã¡ãªã¿ã«åæ¯ã568ã®å Žåã®å¯Ÿæ°ã®è¿äŒŒå€ã¯
log2 â 171/568 â 0.30106
log3 â 271/568 â 0.47711
log5 â 397/568 â 0.69894
log7 â 480/568 â 0.84507
ãªã®ã§ããªãè¯ãè¿äŒŒã«ãªã£ãŠããŸããã
忝ã568ã«ãªããããªçµåããé©åœã«æ¢ããŠã¿ããšã
(2400,2401),(4374,4375),(250000,250047)
ããåŒãç«ãŠãã°äžèšã®å€ã«ãªãããã§ãã
(æ€ç®ããŠããŸããã)
No.2157ãããã2024幎9æ15æ¥ 13:26
ãããŒã568 åªç§ã§ããã
ããã 250047 ã¯äººåããæµç³ã«ã¡ãã£ãšåºãŠããªãâŠâŠã
ãã£ã±ãæ¡æ°ãå€ããš 2 æ°ã®å·®ãå°ããã£ãŠãæ°ã«ãªããªããªã£ãŠããã®ã§ç²ŸåºŠäžããã£ãœãã§ããã
No.2159DD++2024幎9æ15æ¥ 14:35
(3)ã«ã€ããŠ
5log2 + log7 â 2log3 + 2log5
5log2 + log3 + 2log5 â 4log7
log2 + 7log3 â 4log5 + log7
ã
5log2 + log7 + a = 2log3 + 2log5
5log2 + log3 + 2log5 + b = 4log7
log2 + 7log3 + c = 4log5 + log7
ïŒa,b,cïŒ0ïŒ
ãšããŠèšç®ãããš
log2 = (72 - 27a - 5b - 7c) / 239
log3 = (114 + 17a + 12b - 31c) / 239
log5 = (167 + 27a + 5b + 7c) / 239
log7 = (202 - 16a + 59b - 13c) / 239
ãšãªããŸãããã®åŒãã
log2 ïŒ 72/239
log5 ïŒ 167/239
ã¯ãã ã¡ã«ããããŸãããlog3 ãš 114/239 ã®å€§å°é¢ä¿ã¯
17a + 12b - 31c ã®ç¬Šå·ã調ã¹ãªããšããããŸããã
ããã 17a + 12b - 31c ã®ç¬Šå·ã調ã¹ãããã«èšç®ãããš
17a + 12b - 31c = 239log3 - 114log10
ãšãªã£ãŠ 3^239 ãš 10^114 ã®å€§å°é¢ä¿ã調ã¹ãããšã«ãªããæ¬æ«è»¢åã§ãã
ãã£ãŠåæ§ã®æ¹æ³ã§äžçåŒã§äžäžããããããããã«ã¯
è¿äŒŒåŒã倿°çšæããŠããŸããŸå€§å°é¢ä¿ããããããšã«æåŸ
ããããããã
æãã€ããŸãããã远å ã®è¿äŒŒåŒãçšæããããšãããšæ¡æ°ãå¢ããŠ
æèšç®ã«äžåãã«ãªã£ãŠããŸãã®ã§ããšãããã
ããã®æ¹æ³ã§ã®äžçå·ã§ã®è©äŸ¡ã¯é£ããã
ãšèšã£ãŠããããšæããŸãã
No.2160ãããã2024幎9æ16æ¥ 02:52
> 17a + 12b - 31c ã®ç¬Šå·ã調ã¹ãªããšããããŸããã
ãªãã»ã©ãå·®åã宿°åããŠããŸãã°ããã£ãã®ã§ããã
é£ç«æ¹çšåŒãè§£ãæéã¯ãã£ããå¢ããŠããŸããŸãããã©ãã
æã§ãããªãéè¡åçšæããŠè§£ãã®ãäžçªæ©ãããªïŒ
{1/n - 1/(2*n^2)} log e < log{1+(1/n)} < {1/n} log e
ã䜿ãã°ãlog e ã¯æ¬ãåºããŠæŸçœ®ã§ããã®ã§ãa, b, c ã®ç·åçµåã®æ£è² è©äŸ¡ã¯ãªããšããªãã±ãŒã¹ãå€ããã«æããŸãã
(224, 225), (2400, 2401), (4374, 4375) ã®ã±ãŒã¹ã¯å®éããã§ãªããšããªãã¿ããã§ãã
No.2162DD++2024幎9æ16æ¥ 05:03
é·æã§ãã
(2)ã«ã€ããŠ
çŽ æ°2,3,5,7ã10æ¡ä»¥äžã§(2400,2401)ãã誀差çãå°ãããã®ã¯
以äžã®6åãããããŸããã§ããã巊端ã¯èª€å·®ç(倧ããæ¹ã®å€Ã·å°ããæ¹ã®å€ïŒ1)ã§ãã
0.000040616 78121827 78125000
0.000066758 645657712 645700815
0.000107377 3954653486 3955078125
0.000188000 250000 250047
0.000228624 4374 4375
0.000295397 184473632 184528125
0.000416667 2400 2401
78121827 = 3^13 * 7^2, 78125000 = 2^3 * 5^10, å·® = 3173 = 19 * 167
645657712 = 2^4 * 7^9, 645700815 = 3^17 * 5, å·® = 43103 (çŽ æ°)
3954653486 = 2 * 7^11, 3955078125 = 3^4 * 5^11, å·® = 424639 (çŽ æ°)
ããã䜿ã£ãŠ
13log3 + 2log7 = 3log2 + 10log5 (78121827, 78125000)
4log2 + 9log7 = 17log3 + log5 (645657712, 645700815)
log2 + 11log7 = 4log3 + 11log5 (3954653486, 3955078125)
log2 + log5 = 1
ãè§£ããšäžæ¬¡åŸå±ã§è§£ããŸããã§ããã
ãããããŠ
78121827 = 3^13 * 7^2, 78125000 = 2^3 * 5^10, å·® = 3173 = 19 * 167
645657712 = 2^4 * 7^9, 645700815 = 3^17 * 5, å·® = 43103 (çŽ æ°)
250000 = 2^4 * 5^6, 250047 = 3^6 * 7^3, å·® = 47 (çŽ æ°)
ããã䜿ã£ãŠ
13log3 + 2log7 = 3log2 + 10log5 (78121827, 78125000)
4log2 + 9log7 = 17log3 + log5 (645657712, 645700815)
4log2 + 6log5 = 6log3 + 3log7 (250000, 250047)
log2 + log5 = 1
ãè§£ããš
log2 = 171/568, log3 = 271/568, log5 = 397/568, log7 = 480/568
ããã¯èŠèŠãããããŸããã
ããããã®å€ã¯(2400,2401),(4374,4375),(250000,250047)
ãããåŸãããã®ã§ã¯ãªãããšæã£ãŠäžã§ãæ€ç®ããŠããŸããããšæžããã®ã
ãããããŠæ€ç®ããŠã¿ããšããªããš
5log2 + log3 + 2log5 = 4log7 (2400, 2401)
log2 + 7log3 = 4log5 + log7 (4374, 4375)
4log2 + 6log5 = 6log3 + 3log7 (250000, 250047)
log2 + log5 = 1
ã¯äžæ¬¡åŸå±ã§è§£ããŸããã§ãããçµæ§è§£ããªãå ŽåãåºãŠããã®ã§ããã
ããã§ã¯ããããçµåããå€ããŠè©Šãããšã«ããŸãã
13log3 + 2log7 = 3log2 + 10log5 (78121827, 78125000)
log2 + 11log7 = 4log3 + 11log5 (3954653486, 3955078125)
4log2 + 6log5 = 6log3 + 3log7 (250000, 250047)
log2 + log5 = 1
â log2 = 171/568, log3 = 271/568, log5 = 397/568, log7 = 480/568
4log2 + 9log7 = 17log3 + log5 (645657712, 645700815)
log2 + 11log7 = 4log3 + 11log5 (3954653486, 3955078125)
4log2 + 6log5 = 6log3 + 3log7 (250000, 250047)
log2 + log5 = 1
â log2 = 171/568, log3 = 271/568, log5 = 397/568, log7 = 480/568
13log3 + 2log7 = 3log2 + 10log5 (78121827, 78125000)
4log2 + 9log7 = 17log3 + log5 (645657712, 645700815)
log2 + 7log3 = 4log5 + log7 (4374, 4375)
log2 + log5 = 1
â log2 = 171/568, log3 = 271/568, log5 = 397/568, log7 = 480/568
13log3 + 2log7 = 3log2 + 10log5 (78121827, 78125000)
log2 + 11log7 = 4log3 + 11log5 (3954653486, 3955078125)
log2 + 7log3 = 4log5 + log7 (4374, 4375)
log2 + log5 = 1
â log2 = 171/568, log3 = 271/568, log5 = 397/568, log7 = 480/568
13log3 + 2log7 = 3log2 + 10log5 (78121827, 78125000)
4log2 + 6log5 = 6log3 + 3log7 (250000, 250047)
log2 + 7log3 = 4log5 + log7 (4374, 4375)
log2 + log5 = 1
â äžæ¬¡åŸå±
4log2 + 9log7 = 17log3 + log5 (645657712, 645700815)
4log2 + 6log5 = 6log3 + 3log7 (250000, 250047)
log2 + 7log3 = 4log5 + log7 (4374, 4375)
log2 + log5 = 1
â log2 = 171/568, log3 = 271/568, log5 = 397/568, log7 = 480/568
13log3 + 2log7 = 3log2 + 10log5 (78121827, 78125000)
log2 + 7log3 = 4log5 + log7 (4374, 4375)
5log2 + log3 + 2log5 = 4log7 (2400, 2401)
log2 + log5 = 1
â äžæ¬¡åŸå±
è§£ãåŸãããŠãåããã®ã°ããã§ãããã¡ãã£ãšç²ŸåºŠãè¯ããããã ãš
ããŸãå€ãããªãããã§ãã
ã§ã¯ããã«ç²ŸåºŠãè¯ããã®ãèŠã€ããŠè©ŠããŸãã
ãããã10æ¡ä»¥äžãã11æ¡ä»¥äžã12æ¡ä»¥äžãã»ã»ã»ãšå¢ãããŠããªããªãèŠã€ãããŸããã
ã15æ¡ä»¥äžããŸã§å¢ãããŠããã£ãš
0.000026141 205885750000000 205891132094649
0.000033563 281474976710656 281484423828125
ã®äºã€ãèŠã€ãããŸããã®ã§ããããš(78121827, 78125000)ã§è©ŠããŸãã
205885750000000 = 2^7 * 5^9 * 7^7, 205891132094649 = 3^30,
å·® = 5382094649 = 3673 * 1465313
281474976710656 = 2^48, 281484423828125 = 5^11 * 7^8,
å·® = 9447117469 (çŽ æ°)
7log2 + 9log5 + 7log7 = 30log3 (205885750000000, 205891132094649)
48log2 = 11log5 + 8log7 (281474976710656, 281484423828125)
13log3 + 2log7 = 3log2 + 10log5 (78121827, 78125000)
log2 + log5 = 1
â
log2 = 3125/10381 = 0.30103073 (çå€ 0.30103000)
log3 = 4953/10381 = 0.47712166 (çå€ 0.47712125)
log5 = 7256/10381 = 0.69896927 (çå€ 0.69897000)
log7 = 8773/10381 = 0.84510163 (çå€ 0.84509804)
ããããå°ã粟床ãäžãããŸããã
ã¡ãªã¿ã«ããäžæ¡äžã®
0.000007053 2251783932057135 2251799813685248
2251783932057135 = 3^13 * 5 * 7^10, 2251799813685248 = 2^51,
å·® = 15881628113 = 13 * 71 * 17206531
ã䜿ã£ãŠ
13log3 + log5 + 10log7 = 51log2 (2251783932057135, 2251799813685248)
7log2 + 9log5 + 7log7 = 30log3 (205885750000000, 205891132094649)
48log2 = 11log5 + 8log7 (281474976710656, 281484423828125)
log2 + log5 = 1
ãšããŠãäžãšåã忝10381ã®å€ã«ãªããŸããã
ãšããããã§ã
äœ¿ãæ°åã®æ¡æ°ãããªãå¢ãããŠãçµæã®ç²ŸåºŠãããŸãäžãããªãããã
ãšããããšãããããŸããã
No.2167ãããã2024幎9æ16æ¥ 08:53
äœ¿ãæ¡æ°ãäžãã£ãŠãã2, 3, 5, 7 ã§äœããåææ°ã®å²åãæžãããšã§æã¡æ¶ãããŠããŸãã誀差çããªããªãå°ãããªããªããã§ããã
ãããªããšã11ã13ã®äœ¿çšãæ€èšããæ¹ã粟床äžãã«ã¯éèŠãªã®ããªïŒ
No.2168DD++2024幎9æ16æ¥ 13:02
ãŸãé·æã§ããããã§åœåã®èª²é¡ã¯ãšããããå®çµã
(4)
ã11ã远å ããå Žåã
(1äžãŸã§)
0.000102041 9800 9801
0.000228624 4374 4375
0.000330688 3024 3025
0.000416667 2400 2401
0.001244444 5625 5632
9800 = 2^3 * 5^2 * 7^2, 9801 = 3^4 * 11^2
4374 = 2 * 3^7, 4375 = 5^4 * 7
3024 = 2^4 * 3^3 * 7, 3025 = 5^2 * 11^2
2400 = 2^5 * 3 * 5^2, 2401 = 7^4
3log2 + 2log5 + 2log7 = 4log3 + 2log11 (9800, 9801)
log2 + 7log3 = 4log5 + log7 (4374, 4375)
4log2 + 3log3 + log7 = 2log5 + 2log11 (3024, 3025)
5log2 + log3 + 2log5 = 4log7 (2400, 2401)
log2 + log5 = 1
â äžæ¬¡åŸå±
5625 = 3^2 * 5^4, 5632 = 2^9 * 11, å·® = 7
3log2 + 2log5 + 2log7 = 4log3 + 2log11 (9800, 9801)
log2 + 7log3 = 4log5 + log7 (4374, 4375)
5log2 + log3 + 2log5 = 4log7 (2400, 2401)
2log3 + 4log5 = 9log2 + log11 (5625, 5632)
log2 + log5 = 1
â
log2 = 270/897 = 0.301003 (çå€ 0.301030)
log3 = 428/897 = 0.477146 (çå€ 0.477121)
log5 = 627/897 = 0.698997 (çå€ 0.698970)
log7 = 758/897 = 0.845039 (çå€ 0.845098)
log11 = 934/897 = 1.041249 (çå€ 1.041393)
897ã¯äžã®æ¹ã§568ã«æ¬¡ãã§ç²ŸåºŠã®è¯ã忝ã§ãã
(1åãŸã§)
0.000016089 3294172 3294225
0.000022158 67108864 67110351
0.000040616 78121827 78125000
0.000050668 14348180 14348907
3294172 = 2^2 * 7^7, 3294225 = 3^2 * 5^2 * 11^4, å·® = 53 (çŽ æ°)
67108864 = 2^26, 67110351 = 3 * 7^5 * 11^3, å·® = 1487 (çŽ æ°)
78121827 = 3^13 * 7^2, 78125000 = 2^3 * 5^10, å·® = 3173 = 19 * 167
14348180 = 2^2 * 5 * 7^2 * 11^4, 14348907 = 3^15, å·® = 727 (çŽ æ°)
2log2 + 7log7 = 2log3 + 2log5 + 4log11 (3294172, 3294225)
26log2 = log3 + 5log7 + 3log11 (67108864, 67110351)
13log3 + 2log7 = 3log2 + 10log5 (78121827, 78125000)
2log2 + log5 + 2log7 + 4log11 = 15log3 (14348180, 14348907)
log2 + log5 = 1
â
log2 = 6421/21330 = 0.3010314 (çå€ 0.3010300)
log3 = 10177/21330 = 0.4771214 (çå€ 0.4771213)
log5 = 14909/21330 = 0.6989686 (çå€ 0.6989700)
log7 = 18026/21330 = 0.8451008 (çå€ 0.8450980)
log11 = 22213/21330 = 1,0413971 (çå€ 1.0413927)
çµæ§ç²ŸåºŠãäžãããŸããã
ã13ã远å ããå Žåã
(1äžãŸã§)
0.000102041 9800 9801
0.000150263 6655 6656
0.000228624 4374 4375
0.000236742 4224 4225
0.000244200 4095 4096
0.000330688 3024 3025
0.000416667 2400 2401
9800 = 2^3 * 5^2 * 7^2, 9801 = 3^4 * 11^2
6655 = 5 * 11^3, 6656 = 2^9 * 13
4374 = 2 * 3^7, 4375 = 5^4 * 7
4224 = 2^7 * 3 * 11, 4225 = 5^2 * 13^2
4095 = 3^2 * 5 * 7 * 13, 4096 = 2^12
3024 = 2^4 * 3^3 * 7, 3025 = 5^2 * 11^2
2400 = 2^5 * 3 * 5^2, 2401 = 7^4
3log2 + 2log5 + 2log7 = 4log3 + 2log11 (9800, 9801)
log5 + 3log11 = 9log2 + log13 (6655, 6656)
log2 + 7log3 = 4log5 + log7 (4374, 4375)
7log2 + log3 + log11 = 2log5 + 2log13 (4224, 4225)
2log3 + log5 + log7 + log13 = 12log2 (4095, 4096)
log2 + log5 = 1
â äžæ¬¡åŸå±
3log2 + 2log5 + 2log7 = 4log3 + 2log11 (9800, 9801)
log5 + 3log11 = 9log2 + log13 (6655, 6656)
log2 + 7log3 = 4log5 + log7 (4374, 4375)
7log2 + log3 + log11 = 2log5 + 2log13 (4224, 4225)
2log3 + log5 + log7 + log13 = 12log2 (4095, 4096)
4log2 + 3log3 + log7 = 2log5 + 2log11 (3024, 3025)
log2 + log5 = 1
â äžæ¬¡åŸå± (åŒãäžã€å€ããŠããªãäžæ¬¡åŸå±ãªã®ã§ä»ã®åŒãå¿
èŠ)
3log2 + 2log5 + 2log7 = 4log3 + 2log11 (9800, 9801)
log5 + 3log11 = 9log2 + log13 (6655, 6656)
log2 + 7log3 = 4log5 + log7 (4374, 4375)
7log2 + log3 + log11 = 2log5 + 2log13 (4224, 4225)
5log2 + log3 + 2log5 = 4log7 (2400, 2401)
log2 + log5 = 1
â
log2 = 270/897 = 0.301003 (çå€ 0.301030)
log3 = 428/897 = 0.477146 (çå€ 0.477121)
log5 = 627/897 = 0.698997 (çå€ 0.698970)
log7 = 758/897 = 0.845039 (çå€ 0.845098)
log11 = 934/897 = 1.041249 (çå€ 1.041393)
log13 = 999/897 = 1.113712 (çå€ 1.113943)
11ã ã远å ãããšããšåã粟床ã§ãã
(1åãŸã§)
0.000007456 5767125 5767168
0.000008117 123200 123201
0.000013783 72772425 72773428
0.000015573 1990625 1990656
0.000016089 3294172 3294225
0.000018861 19140264 19140625
0.000022158 67108864 67110351
5767125 = 3 * 5^3 * 7 * 13^3, 5767168 = 2^19 * 11, å·® = 43 (çŽ æ°)
123200 = 2^6 * 5^2 * 7 * 11, 123201 = 3^6 * 13^2
72772425 = 3^7 * 5^2 * 11^3, 72773428 = 2^2 * 7^2 * 13^5, å·® = 1003 = 17 * 59
1990625 = 5^5 * 7^2 * 13, 1990656 = 2^13 * 3^5, å·® = 31 (çŽ æ°)
3294172 = 2^2 * 7^7, 3294225 = 3^2 * 5^2 * 11^4, å·® = 53 (çŽ æ°)
19140264 = 2^3 * 3^2 * 11^2 * 13^3, 19140625 = 5^8 * 7^2, å·® = 361 = 19^2
67108864 = 2^26, 67110351 = 3 * 7^5 * 11^3, å·® = 1487 (çŽ æ°)
log3 + 3log5 + log7 + 3log13 = 19log2 + log11 (5767125, 5767168)
6log2 + 2log5 + log7 + log11 = 6log3 + 2log13 (123200, 123201)
7log3 + 2log5 + 3log11 = 2log2 + 2log7 + 5log13 (72772425, 72773428)
5log5 + 2log7 + log13 = 13log2 + 5log3 (1990625, 1990656)
2log2 + 7log7 = 2log3 + 2log5 + 4log11 (3294172, 3294225)
log2 + log5 = 1
â äžæ¬¡åŸå±
log3 + 3log5 + log7 + 3log13 = 19log2 + log11 (5767125, 5767168)
6log2 + 2log5 + log7 + log11 = 6log3 + 2log13 (123200, 123201)
7log3 + 2log5 + 3log11 = 2log2 + 2log7 + 5log13 (72772425, 72773428)
2log2 + 7log7 = 2log3 + 2log5 + 4log11 (3294172, 3294225)
3log2 + 2log3 + 2log11 + 3log13 = 8log5 + 2log7 (19140264, 19140625)
log2 + log5 = 1
â
log2 = 6079/20194 = 0.3010300089 (çå€ 0.3010299957)
log3 = 9635/20194 = 0.4771219174 (çå€ 0.4771212547)
log5 = 14115/20194 = 0.6989699911 (çå€ 0.6989700043)
log7 = 17066/20194 = 0.8451025057 (çå€ 0.8450980400)
log11 = 21030/20194 = 1.0413984352 (çå€ 1.0413926852)
log13 = 22495/20194 = 1.1139447361 (çå€ 1.1139433523)
粟床ã¯11ã ã远å ã®ãšããšåçšåºŠã§ãã
ïŒlog2ãšlog5ã¯ç²ŸåºŠãããã§ãããä»ã¯ãããŸã§è¯ããããŸããïŒ
ã29ãŸã§è¿œå ããå ŽåïŒçŽ æ°10åïŒã
(1åãŸã§)
0.000000010 96059600 96059601
0.000000055 18085704 18085705
0.000000075 26578123 26578125
0.000000084 11859210 11859211
0.000000095 10556000 10556001
0.000000121 8268799 8268800
0.000000155 12901779 12901781
0.000000169 5909760 5909761
0.000000194 5142500 5142501
0.000000244 4096575 4096576
0.000000244 4090624 4090625
0.000000250 4004000 4004001
0.000000315 22194425 22194432
0.000000365 13697019 13697024
0.000000365 90312467 90312500
0.000000371 2697695 2697696
0.000000485 8254125 8254129
0.000000489 88012332 88012375
0.000000494 2023424 2023425
0.000000520 90312453 90312500
0.000000540 1852200 1852201
0.000000560 67874587 67874625
0.000000569 75557027 75557070
0.000000587 46000759 46000786
96059600 = 2^4 * 5^2 * 7^2 * 13^2 * 29, 96059601 = 3^8 * 11^4
18085704 = 2^3 * 3 * 7^3 * 13^3, 18085705 = 5 * 11 * 17 * 23 * 29^2
26578123 = 11 * 13^2 * 17 * 29^2, 26578125 = 3^5 * 5^6 * 7
11859210 = 2 * 3^4 * 5 * 11^4, 11859211 = 7 * 13 * 19^4
10556000 = 2^5 * 5^3 * 7 * 13 * 29, 10556001 = 3^4 * 19^4
8268799 = 7^2 * 11 * 23^2 * 29, 8268800 = 2^10 * 5^2 * 17 * 19
12901779 = 3^2 * 11 * 19^4, 12901781 = 23^2 * 29^3
5909760 = 2^8 * 3^5 * 5 * 19, 5909761 = 11^2 * 13^2 * 17^2
5142500 = 2^2 * 5^4 * 11^2 * 17, 5142501 = 3^3 * 7^2 * 13^2 * 23
4096575 = 3^4 * 5^2 * 7 * 17^2, 4096576 = 2^6 * 11^2 * 23^2
4090624 = 2^8 * 19 * 29^2, 4090625 = 5^5 * 7 * 11 * 17
4004000 = 2^5 * 5^3 * 7 * 11 * 13, 4004001 = 3^2 * 23^2 * 29^2
22194425 = 5^2 * 11^3 * 23 * 29, 22194432 = 2^8 * 3^3 * 13^2 * 19
13697019 = 3^4 * 7^3 * 17 * 29, 13697024 = 2^16 * 11 * 19
90312467 = 7 * 23^2 * 29^3, 90312500 = 2^2 * 5^7 * 17^2
2697695 = 5 * 7^3 * 11^2 * 13, 2697696 = 2^5 * 3^2 * 17 * 19 * 29
8254125 = 3^2 * 5^3 * 11 * 23 * 29, 8254129 = 13^4 * 17^2
88012332 = 2^2 * 3^4 * 17 * 19 * 29^2, 88012375 = 5^3 * 11^3 * 23^2
2023424 = 2^13 * 13 * 19, 2023425 = 3^2 * 5^2 * 17 * 23^2
90312453 = 3^2 * 7 * 11 * 19^4, 90312500 = 2^2 * 5^7 * 17^2
1852200 = 2^3 * 3^3 * 5^2 * 7^3, 1852201 = 13 * 17^3 * 29
67874587 = 11^2 * 23 * 29^3, 67874625 = 3^3 * 5^3 * 7 * 13^2 * 17
75557027 = 7 * 13^3 * 17^3, 75557070 = 2 * 3^3 * 5 * 23^4
46000759 = 7^6 * 17 * 23, 46000786 = 2 * 13^3 * 19^2 * 29
4log2 + 2log5 + 2log7 + 2log13 + log29 = 8log3 + 4log11 (96059600, 96059601)
3log2 + log3 + 3log7 + 3log13 = log5 + log11 + log17 + log23 + 2log29 (18085704, 18085705)
log11 + 2log13 + log17 + 2log29 = 5log3 + 6log5 + log7 (26578123, 26578125)
log2 + 4log3 + log5 + 4log11 = log7 + log13 + 4log19 (11859210, 11859211)
2log7 + log11 + 2log23 + log29 = 10log2 + 2log5 + log17 + log19 (8268799, 8268800)
2log3 + log11 + 4log19 = 2log23 + 3log29 (12901779, 12901781)
8log2 + 5log3 + log5 + log19 = 2log11 + 2log13 + 2log17 (5909760, 5909761)
4log3 + 2log5 + log7 + 2log17 = 6log2 + 2log11 + 2log23 (4096575, 4096576)
6log7 + log17 + log23 = log2 + 3log13 + 2log19 + log29 (46000759, 46000786)
log2 + log5 = 1
â
log2 = 360565/1197771 = 0.3010299966 (çå€ 0.3010299957)
log3 = 571482/1197771 = 0.4771212527 (çå€ 0.4771212547)
log5 = 837206/1197771 = 0.6989700034 (çå€ 0.6989700043)
log7 = 1012234/1197771 = 0.8450981031 (çå€ 0.8450980400)
log11 = 1247350/1197771 = 1.0413927203 (çå€ 1.0413926852)
log13 = 1334249/1197771 = 1.1139433164 (çå€ 1.1139433523)
log17 = 1473796/1197771 = 1.2304488922 (çå€ 1.2304489214)
log19 = 1531654/1197771 = 1.2787536182 (çå€ 1.2787536010)
log23 = 1631038/1197771 = 1.3617277426 (çå€ 1.3617278360)
log29 = 1751618/1197771 = 1.4623980711 (çå€ 1.4623979979)
忝ã®1197771ã¯10000000ãŸã§ã§æã誀差ãå°ãªããªãå€ã§ãã
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No.2170ãããã2024幎9æ16æ¥ 14:15
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No.2175DD++2024幎9æ17æ¥ 02:05
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There are eight gold coins, one of which is a forgery containing radioactive material. The task is to identify this forgery using a series of measurements conducted by technicians with Geiger counters. The problem is structured as follows:
1. Coins: There are 8 gold coins, numbered 1 through 8. Exactly one coin is a forgery.
2. Forgery Characteristics: The forged coin contains radioactive material, detectable by a Geiger counter.
3. Technicians: There are 10 technicians available to perform measurements.
4. Measurement Process:
Each technician selects a subset of the 8 coins for measurement.
The technician uses a Geiger counter to test the selected coins simultaneously.
The Geiger counter reacts if and only if the forgery is among the selected coins.
Only the technician operating the device knows the result of the measurement.
5. Measurement Constraints:
Each technician performs exactly one measurement.
A total of 10 measurements are conducted.
6. Reporting:
After each measurement, the technician reports either "positive" (radioactivity detected) or "negative" (no radioactivity detected).
7. Reliability Issue: Up to two technicians may provide unreliable reports, either due to intentional deception or unintentional error.
8. Objective: Identify the forged coin with certainty, despite the possibility of up to two unreliable reports.
Challenge
The challenge is to design a measurement strategy and analysis algorithm that can definitively identify the forged coin, given these constraints and potential inaccuracies in the technicians' reports.
No.2129Dengan kesaktian Indukmu2024幎9æ8æ¥ 00:09
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"000 000 000 ", 0,0,0,
"110 011 101 ", 6,3,5,
"111 110 001 ", 7,6,1,
"010 100 110 ", 2,4,6,
"011 001 010 ", 3,1,2,
"100 111 011 ", 4,7,3,
"001 101 100 ", 1,5,4,
"101 010 111 ", 5,2,7
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"010 100 110 ", 2,4,6,
"011 001 010 ", 3,1,2,
"001 101 100 ", 1,5,4,
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No.2135Dengan kesaktian Indukmu2024幎9æ10æ¥ 00:47
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No.2136DD++2024幎9æ10æ¥ 04:28
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onst codes = [
"100 111 010 ", // XORçµæ 001
"111 010 110 ", // XORçµæ 011
"010 110 001 ", // XORçµæ 101
"110 001 011 ", // XORçµæ 100
"001 011 101 ", // XORçµæ 111
"011 101 100 ", // XORçµæ 010
"101 100 111 ", // XORçµæ 110
];
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No.2137Dengan kesaktian Indukmu2024幎9æ10æ¥ 16:55
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No.2139Dengan kesaktian Indukmu2024幎9æ10æ¥ 23:06
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z = 000
ãšããŸãããŸãã
a = 100
b = 111
c = 010
d = 110
e = 001
f = 011
g = 101
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f = bâcâd
g = câdâe
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b = eâfâg
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e, f, g, a, b, c, d, z ããšã³ã³ãŒãã㊠10 ãããã«ãããã®ããããããE, F, G, A, B, C, D, Z ãšåä»ããŸãã
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E = aâ¥bâ¥câ¥p(c)
F = bâ¥câ¥dâ¥p(d)
G = câ¥dâ¥eâ¥p(e)
A = dâ¥eâ¥fâ¥p(f)
B = eâ¥fâ¥gâ¥p(g)
C = fâ¥gâ¥aâ¥p(a)
D = gâ¥aâ¥bâ¥p(b)
Z = zâ¥zâ¥zâ¥p(z)
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E=100â¥111â¥010â¥1 âe=001
F=111â¥010â¥110â¥0 âf=011
G=010â¥110â¥001â¥1 âg=101
A=110â¥001â¥011â¥0 âa=100
B=001â¥011â¥101â¥0 âb=111
C=011â¥101â¥100â¥1 âc=010
D=101â¥100â¥111â¥1 âd=110
Z=000â¥000â¥000â¥0 âz=000
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No.2140Dengan kesaktian Indukmu2024幎9æ10æ¥ 23:16
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0,0,0,0,0,0,0,0,0,0
1,0,0,1,1,0,0,1,1,1
0,1,0,1,0,1,0,1,1,0
1,1,0,0,1,1,0,0,0,1
0,0,1,1,0,0,1,1,0,1
1,0,1,0,1,0,1,0,1,0
0,1,1,0,0,1,1,0,1,1
1,1,1,1,1,1,1,1,0,0
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1|1,0,0,1,1,0,0,1,1,1 â1çªãåœé å
2|0,1,0,1,0,1,0,1,1,0 â2çªãåœé å
3|1,1,0,0,1,1,0,0,0,1 â3çªãåœé å
4|0,0,1,1,0,0,1,1,0,1 â4çªãåœé å
5|1,0,1,0,1,0,1,0,1,0 â5çªãåœé å
6|0,1,1,0,0,1,1,0,1,1 â6çªãåœé å
7|1,1,1,1,1,1,1,1,0,0 â7çªãåœé å
10äººã®æè¡è
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"100 111 010 110 001 011 101",
"111 010 110 001 011 101 100",
"010 110 001 011 101 100 111",
"110 001 011 101 100 111 010",
"001 011 101 100 111 010 110",
"011 101 100 111 010 110 001",
"101 100 111 010 110 001 011",
"000 000 000 000 000 000 000",
Minimum Hamming Distance: 12
ãªããäžèšã§ã¯ 21 äžã«ã誀ããªãæè¡è
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Minimum Hamming Distance: 11
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No.2145Dengan kesaktian Indukmu2024幎9æ11æ¥ 21:18
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A,B,C,D,E,F,G,H,I,J,K,L,M
-------------------------
0,0,0,0,0,0,0,0,0,0,0,0,0
1,0,0,1,1,0,1,0,0,1,1,0,1
0,1,0,1,0,1,0,1,0,1,0,1,1
1,1,0,0,1,1,1,1,0,0,1,1,0
0,0,1,0,1,1,0,0,1,0,1,1,1
1,0,1,1,0,1,1,0,1,1,0,1,0
0,1,1,1,1,0,0,1,1,1,1,0,0
1,1,1,0,0,0,1,1,1,0,0,0,1
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A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q
---------------------------------
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
1,0,0,1,0,0,1,0,0,1,1,1,0,1,1,1,0
0,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,1
1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1
0,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,1
1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1
0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0
1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0
17äººã®æè¡è
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