Four sisters named Suvarna, Tara, Uma, and Vibha play a special game where the loser of each round must double the money of all other players from her own share. They played four games total, with each sister losing once in alphabetical order (Suvarna, then Tara, then Uma, then Vibha). After the fourth game, each sister had exactly 32 rupees. How much money did Suvarna start with initially?

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Accepted Answer

To solve this problem, we need to work **backwards** from the final state to the initial state.

From the table provided, we can trace the money each sister had after each game:

After the 4th game (Vibha lost): All sisters have **32 rupees** each.

After the 3rd game (Uma lost): Suvarna had 16, Tara had 16, Uma had 16, and Vibha had 80.

After the 2nd game (Tara lost): Suvarna had 8, Tara had 8, Uma had 72, and Vibha had 40.

After the 1st game (Suvarna lost): Suvarna had 4, Tara had 68, Uma had 36, and Vibha had 20.

Now, to determine how much Suvarna started with, we need to understand what happened in the first game:

When Suvarna lost, she had to double everyone else's money from her share:
- Tara started with 34, so Suvarna gave her 34 more (to reach 68)
- Uma started with 18, so Suvarna gave her 18 more (to reach 36)
- Vibha started with 10, so Suvarna gave her 10 more (to reach 20)

The total amount Suvarna gave away was 34 + 18 + 10 = **62 rupees**

Since Suvarna had 4 rupees left after giving away this 62 rupees, her initial amount must have been:
4 + 62 = **66 rupees**

Therefore, Suvarna started with **66 rupees**.

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