For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
10/15/2013

PROBLEM #1

The towns of Alpha, Beta, and Gamma are equidistant from each other. If a car is three miles from Alpha and four miles from Beta, what is the maximum possible distance of the car from Gamma? Assume the land is flat.

PROBLEM #2

A rhombus, ABCD, has sides of length 10. A circle with center A passes through C (the opposite vertex.) Likewise, a circle with center B passes through D. If the two circles are tangent to each other, what is the area of the rhombus?

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Problems from 10/10/13

PROBLEM #1

If it takes Bill 20 hours to paint a house and it takes George 30 hours, how long will it take if they work together yet independently?

SOLUTION 1

PROBLEM #2

A box contains two coins. One coin is heads on both sides and the other is heads on one side and tails on the other. One coin is selected from the box at random and the face of one side is observed. If the face is heads what is the probability that the other side is heads?

SOLUTION 2

Congratulations to N. Alamelu, Alka Arora, Kishore Balsara, Lalit Doshi and Saba Lateef, who were the winners of the last set of puzzles. Here are two puzzles for one and all!

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