2

Part of 2023/2024 Tournament of Towns

Problems(2)

three hands on a clock.

Source: 45th International Tournament of Towns, Senior O-Level P2, Fall 2023

2. There are three hands on a clock. Each of them rotates in a normal direction at some non-zero speed, which can be wrong. In the morning the long and the short hands coincided. Just in three hours after that moment the long and the mid-length hands coincided. After next four hours the short and the mid-length hands coincided. Will it necessarily occur that all three hands will coincide? Alexandr Yuran

square or not necessarily a square

Source: 45th International Tournament of Towns, Junior O-Level P2, Fall 2023

2. The quadrilateral

A B C D

is convex. Its sides

A B

C D

are parallel. It is known that the angles

D A C

A B D

are equal. Furthermore the angles

C A B

D B C

A B C D

necessarily a square? Alexandr Terteryan