Problems

The sum of digits of a positive integer \(n\) is the same as the number of digits of \(n\). What are the possible products of the digits of \(n\)?

In the triangle \(\triangle ABC\), the angle \(\angle ACB=60^{\circ}\), marked at the top. The angle bisectors \(AD\) and \(BE\) intersect at the point \(I\).

Find the angle \(\angle AIB\), marked in red.

Find, with proof, all integer solutions of \(a^3+b^3=9\).