MathDB

5

Part of 2021 Tuymaada Olympiad

Problems(2)

Tuymaada 2021 / J5

Source: Tuymaada 2021 / J5

7/30/2021
In a 100×100100\times 100 table 110110 unit squares are marked. Is it always possible to rearrange rows and columns so that all the marked unit squares are above the main diagonal or on it?
Sines and Cosines form A.P. and G.P.

Source: Tuymaada 2021 Senior P5.

7/28/2021
Sines of three acute angles form an arithmetic progression, while the cosines of these angles form a geometric progression. Prove that all three angles are equal.
trigonometryalgebraprogressionsarithmetic sequencegeometric sequence