{"id":53360,"date":"2017-10-19T21:44:00","date_gmt":"2017-10-19T18:44:00","guid":{"rendered":"http:\/\/www.lovendal.ro\/wp52\/?p=53360"},"modified":"2017-10-19T21:44:00","modified_gmt":"2017-10-19T18:44:00","slug":"exclusiv-o-poveste-ghicitoare-incredibil-de-complicata-cati-dolari-trebuie-sa-plateasca-bill-lui-john","status":"publish","type":"post","link":"https:\/\/www.lovendal.ro\/wp52\/exclusiv-o-poveste-ghicitoare-incredibil-de-complicata-cati-dolari-trebuie-sa-plateasca-bill-lui-john\/","title":{"rendered":"EXCLUSIV! O poveste-ghicitoare incredibil de complicat\u0103: c\u00e2\u0163i dolari trebuie s\u0103-i pl\u0103teasc\u0103 Bill lui John?"},"content":{"rendered":"

\"\"<\/a>Haide\u0163i s\u0103 vorbim ast\u0103zi despre o problem\u0103-ghicitoare extrem de interesant\u0103, care v\u0103 va pune pu\u0163in (mai mult) creierul la contribu\u0163ie. Povestea pare a fi una simpl\u0103, dar totu\u015fi…<\/p>\n

– Bill \u015fi John sunt doi fra\u0163i fermieri care \u00eempart egal un num\u0103r de vaci. \u00centruc\u00e2t pre\u0163ul laptelui de vac\u0103 a sc\u0103zut mult, cei doi au hot\u0103r\u00e2t s\u0103 v\u00e2nd\u0103 vacile \u015fi s\u0103 cumpere ni\u015fte oi.<\/p>\n

– Ei au luat pentru fiecare vac\u0103 o sum\u0103 de bani egal\u0103 cu num\u0103rul de vaci avute (de exemplu, dac\u0103 au avut 10 vaci, au luat 10 dolari pe vac\u0103, adic\u0103 \u00een total 10 x 10 = 100 de dolari; dac\u0103 au avut 20 de vaci, au luat 20 de dolari pe vac\u0103, adic\u0103 20 x 20 = 400 de dolari).<\/p>\n

– Cu suma luat\u0103 din v\u00e2nzarea vacilor, Bill \u015fi John hot\u0103r\u0103sc s\u0103 cumpere ni\u015fte oi, la pre\u0163ul de 10 dolari pe oaie. Ei cump\u0103rar\u0103 at\u00e2tea oi, c\u00e2t le-a permis suma total\u0103 de bani avut\u0103 la dispozi\u0163ie. La urm\u0103, le-a mai r\u0103mas ni\u015fte dolari, cu care n-au mai putut s\u0103-\u015fi cumpere o oaie, ci doar o c\u0103pri\u0163\u0103.<\/p>\n

– \u00cen final, cei doi fra\u0163i hot\u0103r\u0103sc s\u0103-\u015fi \u00eempart\u0103 \u00een mod egal num\u0103rul de animale; \u00eens\u0103, unul din fra\u0163i (Bill) avea o oaie \u00een plus, iar cel\u0103lalt (John) o c\u0103pri\u0163\u0103 \u00een plus. De\u015fi num\u0103rul de animale \u00eemp\u0103r\u0163it era egal, c\u0103pri\u0163a era mai ieftin\u0103 dec\u00e2t oaia, a\u015fa c\u0103 Bill era avantajat fa\u0163\u0103 de John. Solu\u0163ia care se cere e urm\u0103toarea: c\u00e2\u0163i dolari trebuie s\u0103-i dea Bill lui John, astfel \u00eenc\u00e2t cei doi s\u0103-\u015fi \u00eempart\u0103 \u00een mod egal \u015fi valoric animalele, nu doar \u00een mod cantitativ?<\/p>\n

V\u0102 ROG S\u0102 V\u0102 G\u00c2NDI\u0162I \u00ceNT\u00c2I LA SOLU\u0162IE \u015eI APOI S\u0102 CITI\u0162I REZOLVAREA PROBLEMEI PE CARE O G\u0102SI\u0162I MAI JOS!<\/strong><\/p>\n

 <\/p>\n

REZOLVAREA PROBLEMEI<\/em><\/strong><\/p>\n

De\u015fi la \u00eenceput pare simplu, rezolvarea problemei nu e chiar at\u00e2t de facil\u0103. Trebuie s\u0103 fim aten\u0163i la formularea problemei.<\/p>\n

1) La \u00eenceput ni se spune c\u0103 cei doi fra\u0163i aveau un num\u0103r egal de vaci, pe care \u015fi-l \u00eemp\u0103r\u0163eau \u00eentre ei. A\u015fadar, exist\u0103 la \u00eenceput un num\u0103r par de vaci (2, 4, 6, 8, 10 etc.), care s\u0103 poat\u0103 fi \u00eemp\u0103r\u0163it exact la 2, f\u0103r\u0103 rest.<\/p>\n

2) Apoi, problema-ghicitoare ne spune c\u0103, la v\u00e2nzare, s-a luat pentru fiecare vac\u0103 o sum\u0103 de bani egal\u0103 cu num\u0103rul de vaci avute. Ceea ce \u00eenseamn\u0103 c\u0103 avem de-a face cu p\u0103tratul fiec\u0103rui num\u0103r par, adic\u0103 rezultatul \u00eenmul\u021birii sale cu el \u00eensu\u0219i. S\u0103 lu\u0103m urm\u0103torul tabel de p\u0103trate ale numerelor pare:
\n2 x 2 = 4
\n4 x 4 = 16
\n6 x 6 = 36
\n8 x 8 = 64
\n10 x 10 = 100
\n12 x 12 = 144
\n14 x 14 = 196
\n16 x 16 = 256
\n18 x 18 = 324
\n20 x 20 = 400<\/p>\n

Se poate continua la infinit, dar, desigur, nu are rost.<\/p>\n

3) Acum, \u00eentrebarea care se pune e urm\u0103toarea: care num\u0103r din tabelul de mai sus ar trebui folosit? C\u0103 evident c\u0103 nu toate se potrivesc datelor problemei noastre. S\u0103 le lu\u0103m la r\u00e2nd:<\/p>\n

– Nu e posibil ca cei doi fra\u0163i s\u0103 fi avut 2 vaci<\/strong>, c\u0103ci altfel ar fi ob\u0163inut doar 4 dolari pe ele, iar \u00een problem\u0103 se spune c\u0103 se cump\u0103r\u0103 „oi” (deci, cel pu\u0163in 2 x 10 dolari = 20 dolari) + mai r\u0103m\u00e2ne cel pu\u0163in 1 dolar pentru cump\u0103rarea unei c\u0103pri\u0163e. A\u015fadar, trebuie s\u0103 ne orient\u0103m la un num\u0103r de vaci, care, la p\u0103trat, s\u0103 fie mai mare de 21. \u00cen concluzie, din tabelul de mai sus excludem \u015fi solu\u0163ia cu 4 vaci<\/strong>.<\/p>\n

– \u00cen ceea ce prive\u015fte posibilitatea ca cei 2 fra\u0163i s\u0103 fi avut 6 vaci<\/strong>, pe care s\u0103 le fi v\u00e2ndut cu 6 dolari (6 x 6 = 36), solu\u0163ia e viabil\u0103. Cei doi fra\u0163i \u015fi-au cump\u0103rat cu banii ob\u0163inu\u0163i (36 de dolari), 3 oi pe care au dat 30 de dolari (3 oi x 10 dolari\/oaie = 30) \u015fi le-au mai r\u0103mas 6 dolari, cu care ei au putut s\u0103-\u015fi cumpere o c\u0103pri\u0163\u0103. A\u015fadar, este \u00eendeplinit\u0103 \u015fi condi\u0163ia ca aceast\u0103 capr\u0103 s\u0103 coste mai pu\u0163in de 10 dolari. \u00cen cazul acesta, cei doi fra\u0163i au 4 animale (3 oi \u015fi o capr\u0103), pe care le \u00eempart \u00een mod egal: Bill are 2 animale (2 oi), iar John are \u015fi el 2 animale (1 oaie \u015fi o capr\u0103). Dar, o capr\u0103 cost\u0103 mai pu\u0163in dec\u00e2t o oaie (6 dolari fa\u0163\u0103 de 10 dolari). Bill are o valoare total\u0103 a animalelor de 2 x 10 = 20 de dolari, iar John are o valoare total\u0103 a animalelor de 16 dolari (1 oaie x 10 dolari + 1 capr\u0103 x 6 dolari ) = 16 dolari. Pentru a se egaliza valoarea animalelor, Bill trebuie s\u0103-i ofere lui John 2 dolari. \u00cen final, Bill va avea: 20 dolari – 2 dolari (pl\u0103ti\u0163i lui John) = 18 dolari, iar John: 16 dolari + 2 dolari (primi\u0163i de la Bill ) = 18 dolari. A\u015fadar, toate condi\u0163iile problemei sunt \u00eendeplinite, iar Bill trebuie s\u0103-i pl\u0103teasc\u0103 2 dolari lui John.<\/p>\n

– \u00cen cazul a 8 vaci<\/strong>, s-ar ob\u0163ine 8 x 8 = 64 de dolari. \u00cens\u0103, nu e o solu\u0163ie viabil\u0103, \u00eentruc\u00e2t cu ace\u015fti bani s-ar putea cump\u0103ra 6 oi (6 x 10 dolari\/oaie = 60 de dolari), iar cu restul de 4 dolari s-ar cump\u0103ra o capr\u0103. \u00cens\u0103, num\u0103rul total de animale ar fi 7 (6 oi + 1 capr\u0103), ce nu pot fi \u00eemp\u0103r\u0163i\u0163i \u00een mod egal. A\u015fadar, avem nevoie ca \u00een final s\u0103 fie un num\u0103r par de animale. Acela\u015fi ra\u0163ionament \u00eel avem \u015fi pentru 10 vaci<\/strong> v\u00e2ndute, sau 12 vaci<\/strong> v\u00e2ndute, num\u0103rul de oi \u015fi capre ce pot fi cump\u0103rate fiind, la fel, impar.<\/p>\n

– \u00cen cazul a 14 vaci<\/strong>, pe care cei doi fra\u0163i s\u0103 le fi v\u00e2ndut cu 14 dolari (14 x 14 = 196 dolari), solu\u0163ia e din nou viabil\u0103. Cei doi fra\u0163i \u015fi-au cump\u0103rat cu banii ob\u0163inu\u0163i (196 de dolari), 19 oi pe care au dat 190 de dolari (19 x 10 = 190) \u015fi le-au mai r\u0103mas, din nou, 6 dolari, cu care ei au putut s\u0103-\u015fi cumpere o c\u0103pri\u0163\u0103. La fel, este \u00eendeplinit\u0103 \u015fi condi\u0163ia ca aceast\u0103 capr\u0103 s\u0103 coste mai pu\u0163in de 10 dolari. \u00cen cazul acesta, cei doi fra\u0163i au 20 de animale (19 oi \u015fi o capr\u0103), pe care le \u00eempart \u00een mod egal: Bill are 10 animale (10 oi), iar John are \u015fi el 10 animale (9 oi \u015fi o capr\u0103). Dar, precum spuneam, o capr\u0103 cost\u0103 mai pu\u0163in dec\u00e2t o oaie (6 dolari fa\u0163\u0103 de 10 dolari). Bill are o valoare total\u0103 a animalelor de 20 x 10 = 200 de dolari, iar John are o valoare total\u0103 a animalelor de 196 dolari (19 oi x 10 dolari + 1 capr\u0103 x 6 dolari ) = 196 dolari. Pentru a se egaliza valoarea animalelor, Bill trebuie s\u0103-i ofere lui John 2 dolari. \u00cen final, Bill va avea: 200 dolari – 2 dolari (pl\u0103ti\u0163i lui John) = 198 dolari, iar John: 196 dolari + 2 dolari (primi\u0163i de la Bill ) = 198 dolari. A\u015fadar, toate condi\u0163iile problemei sunt \u00eendeplinite, iar Bill trebuie s\u0103-i pl\u0103teasc\u0103, din nou, 2 dolari lui John.<\/p>\n

– Interesant e faptul c\u0103 \u015fi \u00een cazul a existen\u0163ei a 16 vaci<\/strong>, ra\u0163ionamentul de mai sus se repet\u0103. Cu 256 de dolari (16 x 16), ob\u0163inu\u0163i din v\u00e2nzarea vacilor, se pot cump\u0103ra 25 de oi (25 x 10 = 250), \u015fi r\u0103m\u00e2n, din nou, 6 dolari pentru achizionarea unei capre. Va fi, iar\u0103\u015fi, un num\u0103r par de animale (26), \u015fi, din nou, va exista o diferen\u0163\u0103 de 4 dolari pentru valoarea animalelor \u00een cazul celor doi fra\u0163i. Se ajunge iar\u0103\u015fi la solu\u0163ia ca Bill s\u0103-i pl\u0103teasc\u0103 2 dolari lui John, pentru egalizarea valorilor.<\/p>\n

A\u015fadar, din toate acestea, se poate forma un model, din care se desprinde urm\u0103toarea regul\u0103: sunt viabile toate solu\u0163iile numerelor ale c\u0103ror p\u0103trat se termin\u0103 \u00een cifra 6 (6 x 6 = 36; 14 x 14 = 196; 16 x 16 = 256 etc.). Oricum, oric\u00e2te vaci ar vinde cei doi fra\u0163i, Bill trebuie s\u0103-i pl\u0103teasc\u0103 lui John 2 dolari, aceast\u0103 solu\u0163ie fiind universal valabil\u0103…<\/p>\n","protected":false},"excerpt":{"rendered":"

Haide\u0163i s\u0103 vorbim ast\u0103zi despre o problem\u0103-ghicitoare extrem de interesant\u0103, care v\u0103 va pune pu\u0163in (mai mult) creierul la contribu\u0163ie. Povestea pare a fi una simpl\u0103, dar totu\u015fi… – Bill \u015fi John sunt doi fra\u0163i fermieri care \u00eempart egal un … <\/p>\n

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