Vrijeme: 11:07

Weirdgebra #3

"Kako je moguće da prošli zadatak ima kombinatornu interpretaciju?" Marica je zapitala i uzbudljivo čekala nove Ivicine zadatke. Ovaj puta Ivica malo duže razmišlja o pitanju koje će postaviti Marici. Ipak, sjetio se je jednog zanimljivog zadatka koji je uistinu algebarski, ali poprilično nestandardan. Ivica je zatim rekao Marici:

Odredi zbroj kvadrata prvu znamenke slijeva i prve znamenku zdesna nakon decimalne točke u decimalnom zapisu broja (\sqrt{2}+\sqrt{3})^{1980}

“How is it possible that the previous problem has a combinatorial interpretation?” Marica asked, eagerly awaiting Ivica’s new challenges. This time Ivica thought a little longer about the question he would pose to Marica. Still, he remembered an interesting problem that is truly algebraic, yet quite unconventional. Ivica then said to Marica:

Determine the sum of the square of the first digit from the left and the first digit to the right after the decimal point in the decimal representation of the number (\sqrt{2}+\sqrt{3})^{1980}