Can you solve it? The brain from Ukraine

A young mathematician's brilliant brainteasers

UPDATE: To read the solutions click here

Todays puzzles are mostly written by Arsenii Nikolaiev, a Ukrainian mathematics undergraduate at Trinity College, Cambridge. Arsenii is a former silver medallist at the International Mathematical Olympiad, who, together with his brother Andrii, founded a maths and coding outreach club for Ukrainian schoolchildren, Kvanta, from which the problems below are taken.

Ukraine has a strong tradition in mathematics. In order to ensure that this will continue during and after the war, a group of Ukrainian mathematicians last month announced the creation of the International Centre for Mathematics in Ukraine, an institution that will support high level research and train young scientists. They believe that maths will have a key role to play in the reconstruction of the country once the conflict is over.