Il Passatempo Fratto

Il forum di Base5, dove è possibile postare problemi, quiz, indovinelli, rompicapo, enigmi e quant'altro riguardi la matematica ricreativa e oltre.

Moderatori: Gianfranco, Bruno

Quelo
Livello 7
Livello 7
Messaggi: 716
Iscritto il: ven giu 16, 2006 3:34 pm

Re: Il Passatempo Fratto

Messaggio da Quelo »

Pasquale ha scritto:
lun apr 04, 2022 4:10 pm
Intanto, se Quelo gradisce, avrei confezionato per lui un simpatico primo simmetrico: 1123211
Grazie Pasquale. Lo apprezzo molto :D

Per concludere ecco il $244$
Questo è stato un lavoraccio, non credo che andrò oltre

$\displaystyle \frac{29}{2}+\frac{31}{3}+\frac{37}{4}+\frac{41}{5}+\frac{43}{6}+\frac{46}{7}+\frac{47}{8}+\frac{49}{9}+\frac{53}{10}+\frac{58}{11}+\frac{59}{12}+\frac{61}{13}+\frac{67}{14}+\frac{71}{15}+\frac{73}{16}+\frac{74}{17}+\frac{79}{18}+\frac{81}{19}+\frac{83}{20}+\frac{86}{21}+\frac{87}{22}+\frac{89}{24}+\frac{92}{25}+\frac{93}{26}+\frac{94}{27}+\frac{97}{28}+\frac{101}{30}+\frac{103}{33}+\frac{107}{34}+\frac{109}{35}+\frac{113}{36}+\frac{115}{38}+\frac{116}{39}+\frac{121}{40}+ \\ \displaystyle \frac{125}{42}+\frac{127}{44}+\frac{128}{45}+\frac{131}{48}+\frac{137}{50}+\frac{139}{51}+\frac{141}{52}+\frac{145}{54}+\frac{146}{55}+\frac{149}{56}+\frac{151}{57}+\frac{157}{60}+\frac{158}{63}+\frac{159}{65}+\frac{161}{66}+\frac{163}{68}+\frac{167}{70}+\frac{169}{72}+\frac{172}{75}+\frac{173}{76}+\frac{174}{77}+\frac{179}{78}+\frac{181}{80}+\frac{185}{84}+\frac{186}{85}+\frac{191}{88}+\frac{193}{90}+\frac{194}{91}+\frac{196}{95}+\frac{197}{99}+\frac{199}{100}+ \\ \displaystyle \frac{203}{102}+\frac{205}{104}+\frac{206}{105}+\frac{211}{108}+\frac{213}{110}+\frac{215}{112}+\frac{217}{114}+\frac{218}{117}+\frac{219}{119}+\frac{223}{120}+\frac{227}{126}+\frac{229}{130}+\frac{233}{132}+\frac{242}{133}+\frac{236}{135}+\frac{237}{136}+\frac{239}{140}+\frac{241}{143}+\frac{245}{144}+\frac{251}{150}+\frac{253}{152}+\frac{254}{153}+\frac{257}{154}+\frac{259}{156}+\frac{262}{165}+\frac{263}{168}+\frac{267}{170}+\frac{268}{171}+\frac{269}{175}+ \\ \displaystyle \frac{271}{176}+\frac{277}{180}+\frac{279}{182}+\frac{281}{187}+\frac{283}{189}+\frac{287}{190}+\frac{289}{195}+\frac{293}{198}+\frac{299}{200}+\frac{301}{204}+\frac{303}{208}+\frac{305}{209}+\frac{307}{210}+\frac{311}{216}+\frac{313}{220}+\frac{314}{221}+\frac{316}{225}+\frac{317}{228}+\frac{320}{231}+\frac{329}{234}+\frac{331}{238}+\frac{337}{240}+\frac{339}{247}+\frac{341}{252}+\frac{343}{255}+\frac{347}{260}+\frac{349}{264}+\frac{353}{266}+\frac{359}{270}+ \\ \displaystyle \frac{361}{272}+\frac{362}{273}+\frac{366}{275}+\frac{367}{280}+\frac{368}{285}+\frac{369}{286}+\frac{370}{297}+\frac{371}{300}+\frac{373}{304}+\frac{377}{306}+\frac{379}{308}+\frac{383}{312}+\frac{386}{315}+\frac{387}{323}+\frac{388}{325}+\frac{389}{330}+\frac{391}{336}+\frac{393}{340}+\frac{395}{342}+\frac{397}{350}+\frac{398}{351}+\frac{401}{357}+\frac{403}{360}+\frac{405}{364}+\frac{409}{374}+\frac{415}{378}+\frac{417}{380}+\frac{419}{385}+\frac{421}{390}+ \\ \displaystyle \frac{427}{396}+\frac{428}{399}+\frac{431}{400}+\frac{433}{408}+\frac{435}{418}+\frac{437}{420}+\frac{438}{425}+\frac{439}{429}+\frac{443}{432}+\frac{447}{440}+\frac{449}{442}+\frac{451}{450}+\frac{452}{455}+\frac{457}{456}+\frac{458}{459}+\frac{461}{462}+\frac{463}{468}+\frac{464}{475}+\frac{465}{476}+\frac{467}{494}+\frac{469}{495}+\frac{473}{504}+\frac{479}{510}+\frac{481}{513}+\frac{483}{520}+\frac{484}{525}+\frac{485}{528}+\frac{487}{532}+\frac{491}{540}+ \\ \displaystyle \frac{493}{546}+\frac{497}{550}+\frac{499}{560}+\frac{500}{561}+\frac{503}{570}+\frac{505}{572}+\frac{506}{585}+\frac{509}{594}+\frac{512}{595}+\frac{517}{600}+\frac{521}{612}+\frac{523}{616}+\frac{527}{624}+\frac{529}{627}+\frac{533}{630}+\frac{535}{646}+\frac{537}{650}+\frac{541}{660}+\frac{542}{663}+\frac{508}{665}+\frac{544}{675}+\frac{547}{680}+\frac{553}{684}+\frac{554}{693}+\frac{557}{700}+\frac{563}{702}+\frac{565}{714}+\frac{566}{715}+\frac{569}{720}+ \\ \displaystyle \frac{571}{728}+\frac{574}{741}+\frac{575}{748}+\frac{543}{756}+\frac{579}{760}+\frac{581}{765}+\frac{587}{770}+\frac{589}{780}+\frac{593}{792}+\frac{599}{798}+\frac{601}{816}+\frac{604}{819}+\frac{607}{825}+\frac{609}{836}+\frac{611}{840}+\frac{613}{850}+\frac{614}{855}+\frac{617}{858}+\frac{619}{880}+\frac{621}{884}+\frac{623}{900}+\frac{629}{910}+\frac{631}{912}+\frac{635}{918}+\frac{641}{924}+\frac{932}{935}+\frac{643}{936}+\frac{647}{945}+\frac{471}{950}+ \\ \displaystyle \frac{653}{952}+\frac{655}{969}+\frac{656}{975}+\frac{657}{988}+\frac{659}{990}=450$

Codice: Seleziona tutto

29/2+31/3+37/4+41/5+43/6+46/7+47/8+49/9+53/10+58/11+59/12+61/13+67/14+71/15+73/16+74/17+79/18+81/19+83/20+86/21+87/22+89/24+92/25+93/26+94/27+97/28+101/30+103/33+107/34+109/35+113/36+115/38+116/39+121/40+125/42+127/44+128/45+131/48+137/50+139/51+141/52+145/54+146/55+149/56+151/57+157/60+158/63+159/65+161/66+163/68+167/70+169/72+172/75+173/76+174/77+179/78+181/80+185/84+186/85+191/88+193/90+194/91+196/95+197/99+199/100+203/102+205/104+206/105+211/108+213/110+215/112+217/114+218/117+219/119+223/120+227/126+229/130+233/132+242/133+236/135+237/136+239/140+241/143+245/144+251/150+253/152+254/153+257/154+259/156+262/165+263/168+267/170+268/171+269/175+271/176+277/180+279/182+281/187+283/189+287/190+289/195+293/198+299/200+301/204+303/208+305/209+307/210+311/216+313/220+314/221+316/225+317/228+320/231+329/234+331/238+337/240+339/247+341/252+343/255+347/260+349/264+353/266+359/270+361/272+362/273+366/275+367/280+368/285+369/286+370/297+371/300+373/304+377/306+379/308+383/312+386/315+387/323+388/325+389/330+391/336+393/340+395/342+397/350+398/351+401/357+403/360+405/364+409/374+415/378+417/380+419/385+421/390+427/396+428/399+431/400+433/408+435/418+437/420+438/425+439/429+443/432+447/440+449/442+451/450+452/455+457/456+458/459+461/462+463/468+464/475+465/476+467/494+469/495+473/504+479/510+481/513+483/520+484/525+485/528+487/532+491/540+493/546+497/550+499/560+500/561+503/570+505/572+506/585+509/594+512/595+517/600+521/612+523/616+527/624+529/627+533/630+535/646+537/650+541/660+542/663+508/665+544/675+547/680+553/684+554/693+557/700+563/702+565/714+566/715+569/720+571/728+574/741+575/748+543/756+579/760+581/765+587/770+589/780+593/792+599/798+601/816+604/819+607/825+609/836+611/840+613/850+614/855+617/858+619/880+621/884+623/900+629/910+631/912+635/918+641/924+932/935+643/936+647/945+471/950+653/952+655/969+656/975+657/988+659/990=450
[Sergio] / $17$

Pasquale
Livello 12
Livello 12
Messaggi: 2831
Iscritto il: mer mag 25, 2005 2:14 am

Re: Il Passatempo Fratto

Messaggio da Pasquale »

Molto interessanti gli indizi di Panurgo:
con i 999 numeri disponibili, quante "T" terzine diverse nel rispetto delle regole stabilite si potrebbero costruire?
La somma di tutte le frazioni in gioco ammonterebbe automaticamente all'intero 2T
_________________

\text {   }ciao Immagine ciao
E' la somma che fa il totale (Totò)

Bruno
Livello 10
Livello 10
Messaggi: 1900
Iscritto il: lun nov 21, 2005 6:07 pm
Località: Bologna

Re: Il Passatempo Fratto

Messaggio da Bruno »

Pasquale ha scritto:
lun apr 04, 2022 10:57 pm
Eh, questo è tuo, ma ti ci vuole una fascia da avvolgere intorno al torace :mrgreen:

No no, Pasquale: è così bello che spetta a te, per aver ideato questo gioco :D
(Bruno)

...........................
Invisibile un vento
l'ha apena sfioragia
sospension d'un momento;
e la bola iridessente gera 'ndagia.
{Biagio Marin}
................................................................
Meglio soluzioni sbagliate che risposte esatte.
{Rudi Mathematici}

Quelo
Livello 7
Livello 7
Messaggi: 716
Iscritto il: ven giu 16, 2006 3:34 pm

Re: Il Passatempo Fratto

Messaggio da Quelo »

Se prendiamo come denominatori numeri dispari consecutivi tranne il 15 (già impegnato come prodotto di 3 x 5) arriviamo alla coppia 29, 31 il cui prodotto è 899
In totale sono 7 terzine
[Sergio] / $17$

panurgo
Livello 9
Livello 9
Messaggi: 1441
Iscritto il: sab nov 19, 2005 3:45 pm
Località: Padova

Re: Il Passatempo Fratto

Messaggio da panurgo »

Quelo ha scritto:
mar apr 05, 2022 11:27 am
Se prendiamo come denominatori numeri dispari consecutivi tranne il 15 (già impegnato come prodotto di 3 x 5) arriviamo alla coppia 29, 31 il cui prodotto è 899
In totale sono 7 terzine
$\begin{array}{cC}
p & q & p\cdot q \\
\hline
3 & 331 & 993 \\
5 & 199 & 995 \\
7 & 141 & 987 \\
9 & 109 & 981 \\
11 & 89 & 979 \\
13 & 75 & 975 \\
15 & 61 & 915 \\
17 & 57 & 969 \\
19 & 51 & 969 \\
21 & 47 & 987 \\
23 & 43 & 989 \\
25 & 39 & 975 \\
27 & 37 & 999 \\
29 & 33 & 957
\end{array}$

Quattordici (sempre poche...)
il panurgo

Principio di Relatività: {\bb m} \not \right {\bb M} \ \Longleftrightarrow \ {\bb M} \not \right {\bb m}
"Se la montagna non va a Maometto, Maometto NON va alla montagna"

Pasquale
Livello 12
Livello 12
Messaggi: 2831
Iscritto il: mer mag 25, 2005 2:14 am

Re: Il Passatempo Fratto

Messaggio da Pasquale »

Se lo dici tu Bruno, importante figura del Team di Base5, non posso che ringraziare.
Devo aggiungere che a livello di mia soluzione, elaborata sino alla pubblicazione del "passatempo", avevo trovato sino a quel momento 5 terzine di frazioni + 1 quartina, tali che la somma di ciascun gruppetto fosse un intero, di modo che anche il totale fosse un intero: Quindi, 19 frazioni con somma totale 41 :

(185/168+23/21+3/4+59/56)+( 9/2+17/30+14/15)+(11/5+62/13+67/65)+(61/35+87/28+43/20)+(29/47+37/74+177/94)+(107/60+27/40+253/24) = 4+6+8+7+3+13 = 41

Matematicamente poco o niente, perché avevo affidato la ricerca alla semplice casualità, anche se opportunamente addomesticata.
Ultima modifica di Pasquale il ven apr 08, 2022 8:45 pm, modificato 4 volte in totale.
_________________

\text {   }ciao Immagine ciao
E' la somma che fa il totale (Totò)

Gianfranco
Supervisore del sito
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Iscritto il: ven mag 20, 2005 9:51 pm
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Re: Il Passatempo Fratto

Messaggio da Gianfranco »

Quelo ha scritto:
lun apr 04, 2022 11:38 pm
Questo è stato un lavoraccio, non credo che andrò oltre
Grazie Sergio per il potentissimo lavoro!
Comunque, secondo me, andrai oltre.
Pace e bene a tutti.
Gianfranco

Quelo
Livello 7
Livello 7
Messaggi: 716
Iscritto il: ven giu 16, 2006 3:34 pm

Re: Il Passatempo Fratto

Messaggio da Quelo »

Non ho resistito

$\displaystyle \frac{29}{2}+\frac{31}{3}+\frac{37}{4}+\frac{41}{5}+\frac{43}{6}+\frac{46}{7}+\frac{47}{8}+\frac{49}{9}+\frac{53}{10}+\frac{58}{11}+\frac{\color{Blue}{515}}{12}+\frac{61}{13}+\frac{67}{14}+\frac{71}{15}+\frac{73}{16}+\frac{74}{17}+\frac{79}{18}+\frac{81}{19}+\frac{83}{20}+\frac{86}{21}+\frac{87}{22}+\frac{89}{24}+\frac{92}{25}+\frac{93}{26}+\frac{94}{27}+\frac{97}{28}+\frac{101}{30}+\frac{103}{33}+\frac{107}{34}+\frac{109}{35}+\frac{113}{36}+\frac{115}{38}+\frac{116}{39}+\frac{121}{40}+ \\ \displaystyle \frac{125}{42}+\frac{127}{44}+\frac{128}{45}+\frac{131}{48}+\frac{137}{50}+\frac{139}{51}+\frac{141}{52}+\frac{145}{54}+\frac{146}{55}+\frac{149}{56}+\frac{151}{57}+\frac{157}{60}+\frac{158}{63}+\frac{159}{65}+\frac{161}{66}+\frac{163}{68}+\frac{167}{70}+\frac{169}{72}+\frac{172}{75}+\frac{173}{76}+\frac{174}{77}+\frac{179}{78}+\frac{181}{80}+\frac{185}{84}+\frac{186}{85}+\frac{191}{88}+\frac{193}{90}+\frac{194}{91}+\frac{196}{95}+\frac{197}{99}+\frac{199}{100}+ \\ \displaystyle \frac{203}{102}+\frac{205}{104}+\frac{206}{105}+\frac{211}{108}+\frac{213}{110}+\frac{215}{112}+\frac{217}{114}+\frac{218}{117}+\frac{219}{119}+\frac{223}{120}+\frac{227}{126}+\frac{229}{130}+\frac{233}{132}+\frac{242}{133}+\frac{236}{135}+\frac{237}{136}+\frac{239}{140}+\frac{241}{143}+\frac{245}{144}+\frac{251}{150}+\frac{253}{152}+\frac{254}{153}+\frac{257}{154}+\frac{259}{156}+\frac{262}{165}+\frac{263}{168}+\frac{267}{170}+\frac{268}{171}+\frac{269}{175}+ \\ \displaystyle \frac{271}{176}+\frac{277}{180}+\frac{279}{182}+\frac{281}{187}+\frac{283}{189}+\frac{287}{190}+\frac{289}{195}+\frac{293}{198}+\frac{299}{200}+\frac{301}{204}+\frac{303}{208}+\frac{305}{209}+\frac{307}{210}+\frac{311}{216}+\frac{313}{220}+\frac{314}{221}+\frac{316}{225}+\frac{317}{228}+\frac{320}{231}+\frac{329}{234}+\frac{331}{238}+\frac{337}{240}+\frac{339}{247}+\frac{341}{252}+\frac{343}{255}+\frac{347}{260}+\frac{349}{264}+\frac{353}{266}+\frac{359}{270}+ \\ \displaystyle \frac{361}{272}+\frac{362}{273}+\frac{366}{275}+\frac{367}{280}+\frac{368}{285}+\frac{369}{286}+\frac{370}{297}+\frac{371}{300}+\frac{373}{304}+\frac{377}{306}+\frac{379}{308}+\frac{383}{312}+\frac{386}{315}+\frac{387}{323}+\frac{388}{325}+\frac{389}{330}+\frac{391}{336}+\frac{393}{340}+\frac{395}{342}+\frac{397}{350}+\frac{398}{351}+\frac{401}{357}+\frac{403}{360}+\frac{405}{364}+\frac{409}{374}+\frac{415}{378}+\frac{417}{380}+\frac{419}{385}+\frac{421}{390}+ \\ \displaystyle \frac{427}{396}+\frac{428}{399}+\frac{431}{400}+\frac{433}{408}+\frac{435}{418}+\frac{437}{420}+\frac{438}{425}+\frac{439}{429}+\frac{443}{432}+\frac{447}{440}+\frac{449}{442}+\frac{451}{450}+\frac{452}{455}+\frac{457}{456}+\frac{458}{459}+\frac{461}{462}+\frac{463}{468}+\frac{464}{475}+\frac{465}{476}+\frac{467}{494}+\frac{469}{495}+\frac{473}{504}+\frac{479}{510}+\frac{481}{513}+\frac{483}{520}+\frac{484}{525}+\frac{485}{528}+\frac{487}{532}+\frac{491}{540}+ \\ \displaystyle \frac{493}{546}+\frac{497}{550}+\frac{499}{560}+\frac{500}{561}+\frac{503}{570}+\frac{505}{572}+\frac{506}{585}+\frac{509}{594}+\frac{512}{595}+\frac{517}{600}+\frac{521}{612}+\frac{523}{616}+\frac{527}{624}+\frac{529}{627}+\frac{533}{630}+\frac{535}{646}+\frac{537}{650}+\frac{541}{660}+\frac{542}{663}+\frac{508}{665}+\frac{544}{675}+\frac{547}{680}+\frac{553}{684}+\frac{554}{693}+\frac{557}{700}+\frac{563}{702}+\frac{565}{714}+\frac{566}{715}+\frac{569}{720}+ \\ \displaystyle \frac{571}{728}+\frac{574}{741}+\frac{575}{748}+\frac{543}{756}+\frac{579}{760}+\frac{581}{765}+\frac{587}{770}+\frac{589}{780}+\frac{593}{792}+\frac{599}{798}+\frac{601}{816}+\frac{604}{819}+\frac{607}{825}+\frac{609}{836}+\frac{611}{840}+\frac{613}{850}+\frac{614}{855}+\frac{617}{858}+\frac{619}{880}+\frac{621}{884}+\frac{623}{900}+\frac{629}{910}+\frac{631}{912}+\frac{635}{918}+\frac{641}{924}+\frac{932}{935}+\frac{643}{936}+\frac{647}{945}+\frac{471}{950}+ \\ \displaystyle \frac{653}{952}+\frac{655}{969}+\frac{656}{975}+\frac{657}{988}+\frac{659}{990}=2\cdot244$

[/quote]
[Sergio] / $17$

Gianfranco
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Iscritto il: ven mag 20, 2005 9:51 pm
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Re: Il Passatempo Fratto

Messaggio da Gianfranco »

Quelo ha scritto:
mar apr 05, 2022 7:06 pm
Non ho resistito
Ottimo!
Il tuo post irresistibile è il n. 666
Pace e bene a tutti.
Gianfranco

Quelo
Livello 7
Livello 7
Messaggi: 716
Iscritto il: ven giu 16, 2006 3:34 pm

Re: Il Passatempo Fratto

Messaggio da Quelo »

Gianfranco ha scritto:
mar apr 05, 2022 7:03 pm
Comunque, secondo me, andrai oltre.
E in effetti hai ragione, nuovo record $279$ (numeri da 2 a 999)
Qui però sono stato fortunato

Codice: Seleziona tutto

29/2+31/3+37/4+41/5+43/6+47/7+49/8+53/9+59/10+61/11+67/12+71/13+73/14+74/15+79/16+81/17+83/18+86/19+87/20+89/21+93/22+94/23+97/24+98/25+101/26+103/27+107/28+109/30+113/33+121/34+122/35+125/36+127/38+128/39+129/40+131/42+137/44+139/45+141/46+145/48+147/50+148/51+149/52+151/54+157/55+159/56+160/57+163/60+164/63+166/65+167/66+169/68+172/69+173/70+179/72+181/75+183/76+185/77+191/78+193/80+197/84+199/85+201/88+203/90+205/91+211/92+212/95+214/99+217/100+223/102+227/104+229/105+233/108+237/110+239/112+241/114+242/115+244/117+246/119+251/120+257/126+259/130+263/132+265/133+268/135+269/136+271/138+277/140+278/143+281/144+283/150+287/152+290/153+291/154+293/156+295/161+296/165+305/168+307/170+310/171+311/175+313/176+317/180+319/182+321/184+324/187+326/189+327/190+328/195+329/198+331/200+335/204+337/207+339/208+343/209+347/210+349/216+353/220+354/221+356/225+359/228+361/230+362/231+365/234+367/238+371/240+372/247+373/252+375/253+376/255+379/260+383/264+387/266+389/270+393/272+394/273+397/275+401/276+403/280+404/285+405/286+406/297+407/299+409/300+411/304+413/306+415/308+419/312+421/315+423/322+424/323+426/325+427/330+431/336+433/340+439/342+443/345+447/350+448/351+449/357+301/360+453/364+457/368+461/374+463/378+467/380+471/385+473/390+474/391+479/396+481/399+487/400+491/408+493/414+497/418+499/420+501/425+502/429+503/432+505/437+507/440+509/442+511/450+512/455+515/456+517/459+519/460+521/462+523/468+524/475+529/476+530/483+531/494+533/495+535/504+537/506+539/510+541/513+543/520+544/525+545/528+547/532+551/540+557/546+559/550+563/552+569/560+571/561+577/570+579/572+581/575+583/585+587/594+589/595+591/598+593/600+599/612+601/616+602/621+605/624+607/627+611/630+613/644+615/646+617/650+619/660+620/663+622/665+623/675+631/680+635/684+637/690+640/693+641/700+643/702+647/714+648/715+949/720+653/728+655/741+657/748+659/756+661/759+667/760+668/765+669/770+671/780+673/782+677/792+683/798+687/805+689/816+691/819+692/825+695/828+697/836+701/840+857/850+704/855+707/858+709/874+711/880+713/884+716/897+719/900+723/910+727/918+779/920+731/924+732/935+733/936+772/945+737/950+739/952+743/966+745/969+746/975+649/988+763/990=540
[Sergio] / $17$

Gianfranco
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Re: Il Passatempo Fratto

Messaggio da Gianfranco »

Quelo ha scritto:
mar apr 05, 2022 8:10 pm
E in effetti hai ragione, nuovo record $279$ (numeri da 2 a 999)
Qui però sono stato fortunato
OOOPS! Chiedo scusa, prima avevo aggiunto frazioni che non andavano bene perché superavano il limite di 1000 dato da Pasquale.
Me ne ero dimenticato e pensavo che si potesse arrivare a 2000.
Ho eliminato gli errori nei messaggi precedenti.

Comunque aggiungo queste tre frazioni valide alle tue, quindi il record sale a 282 frazioni.

$\displaystyle \frac{333}{332}+\frac{553}{498}+\frac{883}{996}=3
$
Pace e bene a tutti.
Gianfranco

Quelo
Livello 7
Livello 7
Messaggi: 716
Iscritto il: ven giu 16, 2006 3:34 pm

Re: Il Passatempo Fratto

Messaggio da Quelo »

Interessante, tra i numeri rimasti liberi si possono cercare ulteriori triplette da aggiungere.

Più si va avanti e più si affina la tecnica, adesso siamo a $311$

Codice: Seleziona tutto

31/2+32/3+37/4+41/5+43/6+47/7+49/8+53/9+59/10+61/11+67/12+71/13+73/14+74/15+79/16+81/17+83/18+86/19+89/20+94/21+97/22+98/23+101/24+103/25+107/26+109/27+111/28+113/29+121/30+122/33+123/34+124/35+125/36+127/38+128/39+129/40+131/42+137/44+139/45+141/46+149/48+151/50+155/51+157/52+163/54+164/55+167/56+169/57+173/58+179/60+181/63+183/65+185/66+191/68+193/69+197/70+199/72+202/75+205/76+206/77+211/78+213/80+215/84+217/85+250/87+219/88+223/90+226/91+227/92+229/95+233/99+237/100+239/102+241/104+242/105+245/108+249/110+251/112+257/114+258/115+259/116+262/117+263/119+269/120+271/126+277/130+281/132+282/133+283/135+287/136+289/138+291/140+292/143+293/144+294/145+301/150+303/152+305/153+307/154+311/156+313/161+314/165+317/168+321/170+326/171+329/174+331/175+333/176+337/180+339/182+341/184+343/187+344/189+347/190+349/195+353/198+359/200+361/203+365/204+367/207+369/208+370/209+373/210+379/216+381/220+382/221+383/225+389/228+393/230+394/231+395/232+397/234+401/238+403/240+404/247+407/252+409/253+412/255+413/260+415/261+419/264+421/266+427/270+431/272+484/273+434/275+439/276+443/280+446/285+447/286+449/290+452/297+453/299+457/300+461/304+463/306+465/308+467/312+472/315+474/319+477/322+478/323+479/325+481/330+485/336+487/340+491/342+496/345+497/348+499/350+500/351+502/357+503/360+505/364+507/368+509/374+511/377+515/378+517/380+519/385+521/390+523/391+527/396+529/399+531/400+533/406+535/408+539/414+541/418+547/420+548/425+553/429+557/432+559/435+562/437+563/440+565/442+569/450+571/455+577/456+637/459+583/460+587/462+589/464+593/468+596/475+597/476+599/483+601/493+603/494+604/495+605/504+607/506+611/510+613/513+617/520+619/522+622/525+623/528+625/532+629/540+631/546+633/550+634/551+635/552+639/560+640/561+641/570+643/572+647/575+649/580+652/585+653/594+654/595+655/598+659/600+661/609+671/612+673/616+674/621+677/624+679/627+683/630+685/638+687/644+689/646+691/650+697/660+698/663+699/665+701/667+703/675+707/680+709/684+719/690+722/693+727/696+729/700+731/702+733/714+734/715+737/720+738/725+739/728+740/741+743/748+745/754+751/756+752/759+753/760+757/765+761/770+763/780+767/782+769/783+773/792+775/798+776/805+779/812+781/816+992/819+787/825+791/828+793/836+797/840+801/850+802/855+809/858+811/870+861/874+817/880+821/884+823/897+827/900+829/910+833/912+803/918+837/920+839/924+841/935+847/936+848/945+849/950+851/952+335/957+857/966+859/969+862/975+863/986+865/988+871/990=624
Una volta raggiunto il risultato intero, anche con frazioni riducibili o doppioni nei numeratori, posso sempre sostituire i numeratori a coppie, infatti se due frazioni hanno i denominatori non coprimi, quello che aggiungo ad una posso togliere dall'altra

$\displaystyle \frac{a}{b}+\frac{c}{k\cdot b}=\frac{a}{b}+\frac{d}{b}+\frac{c}{k\cdot b}-\frac{d}{b}=\frac{a+d}{b}+\frac{c-k\cdot d}{k\cdot b}$

Inoltre se il denominatore è minore di 500 posso aggiungere o togliere unità intere
[Sergio] / $17$

Gianfranco
Supervisore del sito
Supervisore del sito
Messaggi: 1459
Iscritto il: ven mag 20, 2005 9:51 pm
Località: Sestri Levante
Contatta:

Re: Il Passatempo Fratto

Messaggio da Gianfranco »

Quelo ha scritto:
mer apr 06, 2022 12:21 am
Più si va avanti e più si affina la tecnica, adesso siamo a $311$
Notevole!
Complimentissimi!
Pace e bene a tutti.
Gianfranco

Quelo
Livello 7
Livello 7
Messaggi: 716
Iscritto il: ven giu 16, 2006 3:34 pm

Re: Il Passatempo Fratto

Messaggio da Quelo »

E siamo a $334$, due terzi dei numeri in gioco.
Inizialmente non pensavo avremmo superato la metà

Codice: Seleziona tutto

29/2+41/3+47/4+53/5+59/6+62/7+71/8+74/9+83/10+86/11+89/12+101/13+107/14+113/15+131/16+116/17+137/18+122/19+149/20+128/21+155/22+134/23+167/24+146/25+173/26+158/27+179/28+191/30+185/32+164/33+197/34+188/35+203/36+215/38+194/39+227/40+233/42+239/44+206/45+251/46+257/48+212/49+263/50+218/51+269/52+281/54+236/55+293/56+248/57+287/60+254/63+278/65+305/66+311/68+284/69+317/70+329/72+296/75+335/76+290/77+341/78+347/80+302/81+353/84+314/85+359/88+371/90+320/91+365/92+326/95+377/96+383/98+332/99+389/100+395/102+401/104+338/105+407/108+413/110+419/112+431/114+344/115+356/117+362/119+443/120+361/121+398/125+449/126+461/130+467/132+508/133+422/135+473/136+479/138+491/140+410/143+485/144+428/147+497/150+503/152+434/153+509/154+515/156+521/160+446/161+527/162+452/165+533/168+551/170+458/171+464/175+545/176+557/180+563/182+569/184+470/187+482/189+581/190+488/195+587/196+593/198+599/200+611/204+512/207+617/208+518/209+629/210+623/216+641/220+524/221+573/224+536/225+647/228+653/230+530/231+659/234+671/238+677/240+683/242+542/245+548/247+689/250+695/252+554/253+566/255+701/260+707/264+713/266+719/270+725/272+578/273+584/275+731/276+737/280+596/285+743/286+749/288+755/294+590/297+426/299+761/300+767/304+773/306+779/308+785/312+614/315+797/322+620/323+791/324+626/325+809/330+803/336+821/340+815/342+632/345+827/350+638/351+839/352+656/357+851/360+662/363+857/364+845/368+863/374+668/375+869/378+881/380+674/385+887/390+686/391+893/392+899/396+386/399+911/400+698/405+905/408+917/414+929/416+923/418+941/420+704/425+710/429+947/432+716/437+953/440+722/441+959/442+971/450+734/455+965/456+640/459+977/460+983/462+989/468+746/475+995/476+31/480+752/483+87/484+93/490+111/494+758/495+123/500+37/504+129/506+43/510+764/513+141/520+776/525+61/528+159/532+788/539+67/540+177/544+73/546+183/550+79/552+201/560+794/561+806/567+97/570+213/572+812/575+818/585+103/588+109/594+824/595+219/598+127/600+842/605+237/608+139/612+243/616+830/621+145/624+848/627+151/630+860/637+249/644+261/646+157/648+267/650+163/660+854/663+866/665+355/672+872/675+279/680+181/684+193/690+878/693+291/700+199/702+205/714+896/715+211/720+217/726+303/728+902/735+309/736+890/741+321/748+223/750+229/756+908/759+327/760+914/765+333/770+241/780+339/782+369/784+235/792+265/798+381/800+926/805+259/810+271/816+932/819+938/825+277/828+944/833+387/836+283/840+956/847+393/850+962/855+289/858+295/864+411/874+1468/875+417/880+307/882+423/884+986/891+998/897+301/900+447/910+313/912+635/918+453/920+331/924+974/931+174/935+337/936+58/945+471/950+435/952+349/966+895/968+64/969+82/975+477/980+489/988+343/990=876
$368$ circa tre quarti

Codice: Seleziona tutto

41/2+47/3+53/4+59/5+71/6+62/7+83/8+74/9+89/10+86/11+101/12+107/13+113/14+122/15+125/16+128/17+131/18+134/19+137/20+146/21+149/22+155/23+167/24+158/25+511/26+164/27+179/28+185/29+191/30+197/32+188/33+215/34+194/35+227/36+233/38+206/39+239/40+251/42+257/44+212/45+263/46+269/48+218/49+281/50+236/51+287/52+293/54+248/55+305/56+254/57+311/58+317/60+278/63+329/64+284/65+335/66+341/68+296/69+347/70+353/72+302/75+359/76+314/77+365/78+371/80+310/81+383/84+332/85+338/87+389/88+401/90+344/91+395/92+356/95+407/96+419/98+362/99+413/100+431/102+443/104+386/105+449/108+461/110+467/112+473/114+398/115+479/116+404/117+384/119+491/120+422/121+485/126+497/130+503/132+428/133+434/135+509/136+515/138+521/140+446/143+527/144+452/145+458/147+533/150+545/152+470/153+557/154+563/156+569/160+482/161+581/162+488/165+587/168+593/170+500/171+599/174+512/175+611/176+617/180+629/182+623/184+518/187+524/189+641/190+635/192+536/195+647/196+653/198+659/200+530/203+671/204+542/207+677/208+548/209+683/210+689/216+701/220+554/221+695/224+566/225+707/228+719/230+578/231+591/232+731/234+737/238+743/240+749/242+584/245+590/247+755/252+596/253+602/255+761/260+614/261+767/264+773/266+779/270+785/272+620/273+626/275+791/276+797/280+632/285+809/286+803/288+821/290+815/294+656/297+662/299+827/300+839/304+845/306+851/308+857/312+668/315+674/319+863/320+869/322+686/323+875/324+691/325+881/330+887/336+893/340+899/342+698/345+905/348+911/350+710/351+917/352+716/357+923/360+722/363+929/364+941/368+947/374+734/377+953/378+959/380+746/385+971/390+740/391+965/392+977/396+752/399+983/400+758/405+989/406+995/408+31/414+93/416+111/418+37/420+764/425+776/429+43/432+788/435+794/437+123/440+806/441+129/442+141/448+61/450+818/455+67/456+824/459+159/460+73/462+177/464+79/468+842/475+183/476+97/480+830/483+201/484+213/490+848/493+219/494+854/495+103/504+237/506+109/510+860/513+243/520+127/522+866/525+139/528+249/532+872/539+151/540+267/544+157/546+279/550+878/551+163/552+291/560+890/561+902/567+169/570+303/572+896/575+181/576+309/580+908/585+193/588+199/594+914/595+321/598+211/600+926/605+327/608+932/609+205/612+333/616+938/621+217/624+944/627+223/630+956/637+339/638+369/644+375/646+229/648+381/650+241/660+974/663+962/665+992/667+235/672+998/675+387/680+259/684+271/690+82/693+265/696+393/700+277/702+411/704+283/714+186/715+289/720+222/725+295/726+417/728+94/735+423/736+106/741+447/748+453/754+307/756+118/759+471/760+124/765+477/770+301/780+465/782+142/783+489/784+313/792+331/798+501/800+246/805+337/810+507/812+343/816+148/819+166/825+349/828+519/832+666/833+531/836+361/840+282/847+537/850+172/855+355/858+367/864+373/870+173/874+549/880+379/882+555/884+922/891+202/897+397/900+573/910+403/912+409/918+579/920+415/924+651/928+318/931+354/935+421/936+214/945+597/950+603/952+226/957+427/960+433/966+615/968+244/969+463/975+633/980+639/986+645/988+439/990=993
[Sergio] / $17$

Gianfranco
Supervisore del sito
Supervisore del sito
Messaggi: 1459
Iscritto il: ven mag 20, 2005 9:51 pm
Località: Sestri Levante
Contatta:

Re: Il Passatempo Fratto

Messaggio da Gianfranco »

Sergio, non ti supera più nessuno!
Pace e bene a tutti.
Gianfranco

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