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Solution to Puzzle L-1.  SOUTH AMERICAN TOUR

Alice, Bill, Carol, David, and Eleonor went to visit several countries in South America.  Each of them visited three of the following countries:  Argentina, Brazil, Chile, Peru and Uruguay.

To solve this puzzle, create a table below with Y representing the countries visited, and X representing the countries not visited.

 

Alice did not visit Argentina.

Bill did not visit Brazil.

Carol did not visit Chile.

David did not visit Peru.

Eleonor did not visit Uruguay.

Based on the above, we start the following table:

 

Argentina

Brazil

Chile

Peru

Uruguay

Alice

X

 

 

 

 

Bill

 

X

 

 

 

Carol

 

 

X

 

 

David

 

 

 

X

 

Eleonor

 

 

 

 

X

Alice is the only one who visited Brazil.

 

Argentina

Brazil

Chile

Peru

Uruguay

Alice

X

Y

 

 

 

Bill

 

X

 

 

 

Carol

 

X

X

 

 

David

 

X

 

X

 

Eleonor

 

X

 

 

X

Since we know the two countries which Carol, David and Eleonor did not visit, we know the three countries each visited.

 

Argentina

Brazil

Chile

Peru

Uruguay

Alice

X

Y

 

 

 

Bill

 

X

 

 

 

Carol

Y

X

X

Y

Y

David

Y

X

Y

X

Y

Eleonor

Y

X

Y

Y

X

Only two of them visited Uruguay.  Therefore, Alice and Bill did not visit Uruguay.

 

Argentina

Brazil

Chile

Peru

Uruguay

Alice

X

Y

 

 

X

Bill

 

X

 

 

X

Carol

Y

X

X

Y

Y

David

Y

X

Y

X

Y

Eleonor

Y

X

Y

Y

X

Now, we know the two countries Alice and Bill did not visit, so we know which three countries they visited.

 

Argentina

Brazil

Chile

Peru

Uruguay

Alice

X

Y

Y

Y

X

Bill

Y

X

Y

Y

X

Carol

Y

X

X

Y

Y

David

Y

X

Y

X

Y

Eleonor

Y

X

Y

Y

X

 

From the table above, we know that:

Alice visited Brazil, Peru and Chile.

Bill visited Argentina, Chile and Peru.

Carol visited Argentina, Peru and Uruguay.

David visited Argentina, Chile and Uruguay.

Eleonor visited Argentina, Chile and Peru.

 

  

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Bits and Beyond...

FERMAT'S LAST THEOREM

Fermat's Last Theorem is one of the famous problems of Mathematics.  This problem was formulated by Pierre de Fermat before his death.  He was a lawyer by profession, who enjoyed spending his leisure time studying mathematics.  This problem when restated is:

If n is a whole number greater than 2, then there are no whole numbers a, b, c such that

an + bn = cn.

For over 350 years, the proof or disproof of this conjecture occupied the minds of mathematicians.  In fact, several more important or useful theories were derived in the effort to prove this theorem.  It was in the recent years that Andrew Wiles, a mathematician from Princeton, proved this theory in a work consisting of more than 200 pages.

 

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