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neruku
postare Oct 8 2011, 12:20 PM
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Mai am 2 probleme:

1. "Cate pag are o carte pentru paginarea careia s-au folosit 4797 cifre??"


2."Determinati nr. naturale abc care verifica relatia abc=ab+bc+ca."

























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marimaria
postare Oct 8 2011, 02:26 PM
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sper sa nu gresesc....rezultatul e 2403 pagini

4797-9 (paginile cu o singura cifra) = 4788
4788/2 (paginile cu doua cifre) = 2394
readunam la asta 9 (paginile cu o sg cifra) si rezultatul e 2403


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ynady
postare Oct 21 2011, 06:31 PM
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QUOTE(neruku @ Oct 8 2011, 01:20 PM) *
Mai am 2 probleme:

1. "Cate pag are o carte pentru paginarea careia s-au folosit 4797 cifre??"
2."Determinati nr. naturale abc care verifica relatia abc=ab+bc+ca."


1. Paginarea cartii incepe cu cifra 1 si continua cu 2, 3 ...etc pana la cifra 9

Deci, se folosesc 9 cifre pentru primele 9 pagini.

In continuare, se folosesc numere formate din 2 cifre, de la nr. 10 la 99. In total 2cifre*90 pagini=180 cifre

Apoi, se folosesc numere formate din 3 cifre, de la pagina 100 la pagina 999. In total 3cifre*900pagini=2700 cifre

Pana acum s-au folosit 9+180+2700=2889 de cifre

Au mai ramas de folosit 4797-2889=1908 cifre
Aceste 1908 cifre vor forma numere din 4 cifre, respectiv 1908:4=477 , adica se vor numerota 477 pagini

In total cartea are 9+90+900+477=1476 pagini


2.abc=ab+bc+ca

a*100+b*10+c=a*10+b+b*10+c+c*10+a
b+10*c=89*a
a nu poate fi 0
Daca a ar fi mai mare sau egal ca 2, relatia ar deveni b+10c >= 178. Deoarece b si c sunt cifre ( 0, 1,2 ...maxim 9), presupunand ca ambele ar fi 9, b+10c= 99. Deci a nu poate fi mai mare sau egal ca 2. Deci a=1.
Relatia devine b+10c=89
Daca c ar fi 9, b ar fi un umar negativ.
Daca c ar fi mai mic sau egal ca 7, atunci b ar fi mai mare sau egal ca 19, deci c nu poate fi decat 8.

Asadar b este 9.

Verifica relatia 198=19+98+81
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postare Jul 7 2017, 04:12 AM
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postare Jul 8 2017, 05:19 AM
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postare Nov 25 2017, 06:10 AM
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postare Apr 9 2018, 08:01 AM
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