Roman Number Equation

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?




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You cant throw away the expensive pills. What will you do now?

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If,
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Based on similar logic, Can you prove that the below algebraic equation is true?
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There are five people. One of them shot and killed one of the other five.
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Consider yourself to be a famous detective "Sherlock Homles", Can you find the killer?

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Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
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If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
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