For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
03/17/2009

FOR STUDENTS

PROBLEM # 1

You have nine pearls, eight are real and one is fake. All the real ones weigh the same and the fake weighs less than the real ones. Using a balance scale , how many times do you need to weigh them in order to weed out the fake pearl?

FOR GROWNUPS

PROBLEM #2

There is a free gift in my breakfast cereal. The manufacturers say that the gift comes in four different colors, and encourage one to collect all four (thus eating lots of cereal). Assuming there is an equal chance of getting any one of the colors, what is the expected number of boxes I must consume to get all four?

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Problem Solutions 03/05/09

PROBLEM # 1
What is the volume of an tetrahedron with edge length of 1?

Solution:

sqrt(2))/12.

PROBLEM # 2
At McDonalds you can order Chicken McNuggets in boxes of 6, 9, and 20. What is the largest number such that you can not order any combination of the above to achieve exactly the number you want?

Solution:
43.

Congratulations to Shailesh Goregaokar and Suhas Joglekar, who were the winner of the last set of puzzles.

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