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For The Mathematically Inclined

Anil Saigal
10/31/2012

Problem 1


Twenty-seven identical white cubes are assembled into a single cube, the outside of which is painted black.  The cube is then disassembled and the smaller cubes thoroughly shuffled in a bag.  A blindfolded man (who cannot feel the paint) reassembles the pieces into a cube.  What is the probability that the outside of this cube is completely black?

Problem 2

A fair coin is tossed n times and the outcome of each toss is recorded.  Find the probability that in the resulting sequence of tosses a head immediately follows a head exactly h times and a tail immediately follows a tail exactly t times.


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Please send your solutions to mr.asaigal@gmail.com.

Use Problem Solutions M-110812 as the subject line. Please include your full name in the text of the main message. Everyone with the right answer will be acknowledged in the next issue of Lokvani.

Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com.

If you need clarification on any problem, please contact anil@lokvani.com.

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