CONCURS #021
14.03.2022, ora 20:00Problema 1 [261 puncte]
$Calculati\ 257\cdot 897-257\cdot 895.$
Problema 2 [322 puncte]
$Daca\ x\ este\ cu\ 3\ mai\ mare\ decat\ y,\ iar\ y\ cu\ 7\ mai\ mic\ decat\ z\ si\ x+y+z=40, $$calculati\ x\cdot y\cdot z.$
Problema 3 [383 puncte]
$Cate\ numere\ naturale\ dau\ catul\ 17\ prin\ impartirea\ la\ 67?$
Problema 4 [444 puncte]
$Aflati\ cate\ numere\ de\ doua\ cifre\ au\ suma\ cifrelor\ egala\ cu\ 12.$
Problema 5 [505 puncte]
$Cate\ numere\ de\ forma\ \overline{xy3z}\ sunt\ divizibile\ cu\ 2?$
Problema 6 [566 puncte]
$Determinati\ suma\ numerelor\ n\ pentru\ care\ 2\cdot n+1\ divide\ pe\ 3\cdot n+17.$
Problema 7 [627 puncte]
$Se\ dau\ numerele\ 2^{1},\ 2^{2},\ 2^{3},\ ...,\ 2^{30}.\ In\ cate\ moduri\ putem\ alege$$trei\ numere\ a\ <\ b\ <\ c\ dintre\ acestea\ astfel\ incat\ c\ >\ a+b?$
Problema 8 [688 puncte]
$Pentru\ cate\ valori\ ale\ lui\ n,\ numerele\ n+5\ si\ n+149\ sunt\ simultan\ patrate\ perfecte?$