A clean, beautifully designed A4 educational mathematics cheat-sheet and solution guide for Grade 6 olympiad math, printable layout on a crisp white paper background. Header in Russian: 'Блок 4. Теория и подробные решения задач'. The page is structured into well-organized visual modules with diagrams, math formulas, step-by-step solutions, and key takeaways: 1. Theory block at top with concise rules on НОК (LCM), gear tooth ratios, and circular motion velocity subtraction (V_rel = V1 - V2). 2. Section 10: Solution for the two meshed gears (36 and 54 teeth) showing LCM(36,54)=108, calculating revolutions 108/36=3 and 108/54=2 with gear diagrams. 3. Section 11: Solution for three gears in a row (20, 28, 35) showing LCM(20,28,35)=140, Gear A = 7 turns, and alternating rotation directions (A clockwise -> B counter-clockwise -> C clockwise). 4. Section 12: Circular track solution (600m, 15 m/s, 10 m/s) with distance/speed calculation t=600/5=120s and period LCM calculation LCM(40,60)=120s. Modern textbook infographic aesthetic, neat callout boxes, colored badges for answers, crisp Cyrillic typography, high resolution, minimalist and sharp layout.
