Prin sume Gauss:
200+ 199 -198-197+196+195-194-193+...............+8 +7-6 -5 +4+3-2-1=
=(3+7+11+...+199)+(4+8+12+...+200)-(1+5+9+...+197)-(2+6+10+...+198)=
={(199+3)[(199-3):4+1]:2} + {(200+4)[(200-4):4+1]:2} -{(197+1)[(197-1):4+1]:2} -{(198+2)[(198-2):4+1]:2} =
=202*50:2 + 204*50:2 - 198*50:2 - 200*50:2 =
=202*25+204*25-198*25-200*25=
=25*(202+204-198-200)=
=25*8=
=200
Sau :
200+ 199 -198-197+196+195-194-193+...............+8 +7-6 -5 +4+3-2-1=
=(200+ 199 -198-197)+(196+195-194-193)+...............+(8 +7-6 -5 )+(4+3-2-1)=
=4+4+...+4+4= 50*4=200
de ce 50? pentru ca am observat seturi de cate patru numere care au ca rezultat=4
200: 4=50 de seturi
