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2017-04-17 Basic

         

The diagonal lines join a vertex to the midpoint of the edge.

What fraction of the regular hexagon is shaded?

5 years ago, the ratio of a father's and his son's ages was 3:1.
15 years from now, the ratio will be 2:1.

What is the father's current age?

I have 3 nickels, 2 dimes, 2 quarters, and 2 half-dollars in my pocket.

If I randomly pull out 4 coins simultaneously, what's the probability that exactly 2 nickels are included?

\(\)
Note: Nickels, dimes, quarters, and half-dollars are all American coins.

If \(a, b,\) and \(c\) are distinct numbers, is it possible that

\[ a + 2b < b + 2c < c + 2a ? \]

You have an empty notebook with 96 sheets. Each sheet is numbered on both sides, with the page numbers ranging from 1 to 192 (inclusive).

Is it possible to rip out 25 sheets such that the sum of the page numbers on these sheets is exactly 1990?

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