Detailed Explanation:

Answer: Option 2 — Only two

The 44th Chess Olympiad 2022 was indeed India's first time hosting this prestigious event, held in Mamallapuram near Chennai. The official mascot was correctly named 'Thambi' (Tamil for younger brother). However, the trophies are reversed: the Open section receives the Hamilton-Russell Cup, while the Women's section receives the Vera Menchik Cup (named after the first Women's World Chess Champion).

✅ Statement 1 – Correct: The 44th Chess Olympiad 2022 was the first time India hosted this event, held in Mamallapuram/Chennai from July 28 to August 9, 2022.
✅ Statement 2 – Correct: The official mascot was named 'Thambi', a Tamil word meaning 'younger brother', representing Tamil Nadu's culture and hospitality.
❌ Statement 3 – Incorrect: The Open section trophy is the Hamilton-Russell Cup, not the Vera Menchik Cup.
❌ Statement 4 – Incorrect: The Women's section trophy is the Vera Menchik Cup, not the Hamilton-Russell Cup.

📝 Short Notes: Chess Olympiad Trophies

• 44th Chess Olympiad 2022: First held in India at Mamallapuram, Tamil Nadu (July 28 – August 9, 2022)
• Record Participation: Nearly 190 teams in Open and over 160 teams in Women's section
• First-ever Torch Relay: The Olympic torch was carried across multiple Indian cities before the event
• Multiple Indian Teams: As host nation, India fielded multiple teams in both sections
• Winners 2022: Open section - Uzbekistan; Women's section - Ukraine