BG-JBMO-TST 2017

Given is a triangle $ABC$ and let $AA_1$ , $BB_1$ be angle bisectors. It turned out that $\angle AA_1B=24^{\circ}$ and $\angle BB_1A=18^{\circ}$ . Find the ratio $\angle BAC:\angle ACB:\angle ABC$ .

Solve the following equation over the integers $$25x^2y^2+10x^2y+25xy^2+x^2+30xy+2y^2+5x+7y+6= 0.$$

Given are sheets and the numbers $00, 01, \ldots, 99$ are written on them. We must put them in boxes $000, 001, \ldots, 999$ so that the number on the sheet is the number on the box with one digit erased. What is the minimum number of boxes we need in order to put all the sheets?