I walk into a restaurant for lunch and my check comes to π dollars. The restaurant will only accept the exact amount -- nothing more, nothing less. What are my options?
(source: quora.com)
My personal favorite solution is this:
Get a square paper and inscribe a circle in it (Diameter of circle = length of square). Blindfold your host and ask him to randomly pick a point on the paper. Tell him that he gets $4 if that point is inside the circle - and gets nothing otherwise.
The probability of getting the point inside the circle is pi/4. Hence, the the host's expectation (expected dollar amount he receives) is exactly equal to pi dollars.
Fair deal !
Another solution is to get a metal (gold, silver, whatever) sheet which costs $1 per sq. inch. Cut out a circle of radius 1 inch from this sheet. The cost of this circular cut-out will be pi*((radius)^2)*cost = pi dollars exactly!
Can you come up with other creative solutions?
(source: quora.com)
My personal favorite solution is this:
Get a square paper and inscribe a circle in it (Diameter of circle = length of square). Blindfold your host and ask him to randomly pick a point on the paper. Tell him that he gets $4 if that point is inside the circle - and gets nothing otherwise.
The probability of getting the point inside the circle is pi/4. Hence, the the host's expectation (expected dollar amount he receives) is exactly equal to pi dollars.
Fair deal !
Another solution is to get a metal (gold, silver, whatever) sheet which costs $1 per sq. inch. Cut out a circle of radius 1 inch from this sheet. The cost of this circular cut-out will be pi*((radius)^2)*cost = pi dollars exactly!
Can you come up with other creative solutions?
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