CONCURS #008
14.02.2022, ora 20:00La rezultat trebuie trecut doar numarul.
Problema 1 [299 puncte]
$Aflati\ cel\ mai\ mic\ numar\ de\ trei\ cifre,\ care\ impartit\ la\ 19\ da\ restul\ 7.$
Problema 2 [398 puncte]
$Fie\ \overline{abc}\ cel\ mai\ mare\ patrat\ perfect\ de\ trei\ cifre.\ Calculati\ a\cdot b\cdot c.$
Problema 3 [497 puncte]
$Un\ bloc\ are\ apartamente\ cu\ 3\ si\ 4\ camere,\ in\ total\ 45\ apartamente\ si\ 163\ camere.$
$Cate\ apartamente\ sunt\ cu\ cate\ 4\ camere?$
Problema 4 [596 puncte]
$Numerele\ de\ la\ 1\ la\ 100\ se\ impart\ la\ 7,\ si\ se\ calculeaza\ suma\ resturilor\ obtinute.$
$Aflati\ aceasta\ suma.$
Problema 5 [695 puncte]
$Fie\ N=12^{n+1}+3\cdot 3^{n}\cdot 2^{2n}+4^{n}\cdot 3^{n},\ unde\ n\ este\ un\ numar\ natural\ nenul.$
$ Aflati\ cel\ mai\ mare\ divizor\ de\ doua\ cifre\ al\ lui\ N.$
Problema 6 [794 puncte]
$Fie\ p\ si\ q\ numere\ prime\ astfel\ incat\ p+q\cdot (q+1) = 308.\ Aflati\ p^{2}+q^{2}.$
Problema 7 [893 puncte]
$Aflati\ numarul\ x\ din\ egalitatea:\ (\overline{ab}-\overline{ba}):(a-b)+3\cdot x=2022,\ unde\ a,b\ cifre\ cu\ a>b.$
Problema 8 [992 puncte]
$La\ numerotarea\ paginilor\ unei\ carti\ s-au\ folosit\ 1170\ de\ cifre.Cate\ pagini\ are\ cartea?$