Question

"Suma unor numere naturale consecutive este 90. Afla numerele. Cate solutii sunt?"

Am descoperit doua solutii (29,30,31) si (21,22,23,24). Am inteles ca sunt 4 solutii, dar nu reusesc sa le descopar pe celelalte doua solutii. Sper sa ma puteti ajuta! Multumesc!

Answer 1

prima solutie: 29,30,31
a doua solutie: 21,22,23,24
a treia solutie: 16,17,18,19,20
a patra solutie: 10,11,12,13,14,15,16,17


Coroana? :(

Answer 2

suma a 3 nr consecutive :
x+x+1+x+2=3x+3=90=>3x=87=>x=29
x+1=30 ; x+2=31 => (29;30;31)
suma a 4 nr consecutive :
x+x+1+x+2+x+3=90=>4x+6=90=>4x=84=>x=21
x+1=22 ; x+2=23 ; x+3=24 => (21;22;23;24)
suma a 12 nr consecutive :
x+x+1+x+2+x+3+x+4+x+5+x+6+x+7+x+8+x+9+x+10+x+11=90=>12x+66=90=>12x=24=>x=2
x+1=3;x+2=4;x+3=5;x+4=6;x+5=7;x+6=8;x+7=9;x+8=10;x+9=11;x+10=12;x+11=13 => (2;3;4;5;6;7;8;9;10;11;12;13)
suma a 24 nr consecutive :
x+x+1+x+2+x+3+x+4+x+5+x+6+x+7+x+8+x+9+x+10+x+11+x+12+x+13+x+14+x+15+x+16+x+17+x+18+x+19+x+20+x+21+x+22+x+23=90=>24x+253=90
=>nu se poate mai departe