Instructions:
1. Speed of anything leaving/in batman's hand: 300 km/s.
2. Speed of anything leaving/in superman's hand: 200 km/s
3. Length of rope of superman = 20 km.
4. Length of rope of batman = 500 km.
5. Mass of object=100 kg,mass of car=1000 kg.
6. They are on a planet where g = 100 km/s^2 and radius=500 km
Games:
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There are 3 games.
Case 1:
Batman or Superman does not win any of the games. Result: 0
Case 2:
Batman wins 1, Superman wins 2 or vice versa. Result: 2
Case 3:
Batman wins 1, Superman wins 1, they both do not win the remaining game. Result: 1
There are 3 cases and there are 3 guesses. Hence, it is guaranteed that at least one of the guesses will be correct.