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Numarul de cifre si divizibilitate cu trei

 
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Andi Brojbeanu
Newton


Joined: 22 Mar 2009
Posts: 383
Location: Targoviste (Dambovita)

PostPosted: Sun Apr 19, 2009 5:16 pm    Post subject: Numarul de cifre si divizibilitate cu trei Reply with quote

Fie n=1234567891011....1997. Cate cifre are n? Determinati cifra de pe locul 1997 si stabiliti daca n se divide cu 3.

Probleme date la olimpiade, RMT 1/1998.
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salazar
Thales


Joined: 06 Apr 2009
Posts: 100
Location: Alba Iulia

PostPosted: Sun Apr 19, 2009 8:23 pm    Post subject: Reply with quote

1\longrightarrow9=9 numere si 9 cifre
10\longrightarrow99=90 numere si 180 de cifre
100\longrightarrow 999=900 numere si 2700 de cifre
1000\longrightarrow 1997=998 numere si 3992 de cifre
in total 6881 de cifre
1000\longrightarrow 1997 sunt 998 de cifre si 49 de numere si rest 2, deci urmatoarele doua cifre vor intra in componenta unui nou numar.
cum urmatorul numar va fi 1049, cifra cautata este 0.
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