1

Part of 2013 Saint Petersburg Mathematical Olympiad

Problems(2)

St.Peterburg, P1 Grade 11, 2013

Source:

Find the minimum positive noninteger root of

\sin x=\sin \lfloor x \rfloor

trigonometryfloor functioncalculusintegrationalgebra proposedalgebra

Interesting number

Source: St Petersburg Olympiad 2013, Grade 10, P1

A

as interesting if

A

is divided by every number that can be received from

A

by crossing some last digits. Find maximum interesting number with different digits.