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Solution to Puzzle 79.  MEMORIAL DAY GATHERING

During a Memorial Day weekend, four veterans, Allan, Bill, Carl and Dan, had their reunion.  They exchanged stories about their previous missions in the Navy.  Each of them has served on two different types of naval vessels.  The two who served on an aircraft carrier together never served on the submarine the other two served together.  The two who served on a destroyer together never served on the cruiser the other two served together.  Carl and Dan had served on the same ship together.  After Allan and Bill served on the same ship together, Allan and Dan served on another ship together.  Allan never served on a destroyer.  Carl and Bill never served on an aircraft carrier.

Based on the information above, fill in the following blanks:

Allan had served on a ________ and a ___________.
Bill had served on a _________ and a ___________.
Carl had served on a ________ and a ___________.
Dan had served on a _________ and a ___________.

Solution:

From the above information, we know that 2 served on an aircraft carrier, 2 served on a submarine, 2 served on a destroyer,  2 served on a cruiser.  

From the final statement "Carl and Bill never served on an aircraft carrier" and the statement "The two who served on an aircraft carrier together never served on the submarine the other two served together", we can conclude that Carl and Bill has served on an submarine while the other two Allan and Dan served on a aircraft carrier.  

The other remaining type of ships are destroyer and cruiser.  We also know that "Allan and Bill served on the same ship together" which may either be the destroyer or the submarine.  Since "Allan never served on a destroyer" Allan and Bill must have served on a cruiser together.  From the statement "The two who served on a destroyer together never served on the cruiser the other two served together", we conclude that the other two, Carl and Dan, served on a destroyer.

Therefore to summarize:

Allan had served on a aircraft carrier and a cruiser.
Bill had served on a submarine and a cruiser.
Carl had served on a submarine and a destroyer.
Dan had served on a aircraft carrier and a destroyer.

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Bits and Beyond...

PRIME NUMBERS

Prime numbers have captured the hearts of many mathematicians for centuries.  During 18th century, mathematician Christian Goldbach (1690-1764) wrote to Leonhard Euler that he believed it could be shown that every even integer greater than 2 is the sum of 2 primes.  For example, 30 = 23+7 and  36 = 13+23.  Until now, this conjecture has neither been proved or disproved.

 

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