How to Solve Logic Problems

The simplest (not to say easiest nor necessarily quickest) way to solve these problems is with a table like the one below.  Let's look at an example and work it through, shall we?

Four brothers go to a dance.

The first thing to do is to set up a chart showing all the possibilities, and then take out the ones we know are wrong. (As Sherlock Holmes would say, "Once one rules out all the impossibilities, whatever is left - however improbable it may seem - will be the truth."  We're going to rule out the impossibilities one by one.)

No brother took his own hat or coat, so the first thing we do is red out those boxes.

Maurice's
Hat
Adiel's
Hat
Art's
Hat
Jerome's
Hat
Maurice's
Coat
Adiel's
Coat
Art's
Coat
Jerome's
Coat
Maurice
                 
Adiel
                 
Art
                 
Jerome
                 
We know that Art took Jerome's hat, so we check that box and red out the other hats and coats for Art.  This also means that Art didn't take Jerome's or his own coat, so we red those boxes, as well as the other brothers' boxes for Jerome's hat.
Maurice's
Hat
Adiel's
Hat
Art's
Hat
Jerome's
Hat
Maurice's
Coat
Adiel's
Coat
Art's
Coat
Jerome's
Coat
Maurice
                 
Adiel
                 
Art
     
X
         
Jerome
                 
Adiel's coat was taken by the Maurice hat-taker, who isn't Art, so Art took Maurice's coat (because that's the only other coat left for him).  Now we check that box, as well as redding out the boxes for the other brothers with Maurice's coat.
 
Maurice's
Hat
Adiel's
Hat
Art's
Hat
Jerome's
Hat
Maurice's
Coat
Adiel's
Coat
Art's
Coat
Jerome's
Coat
Maurice
                 
Adiel
                 
Art
     
X
  X      
Jerome
                 

Adiel didn't take his own coat, so he also didn't take Maurice's hat (they were taken by the same brother) - we red out that box now.
 

Maurice's
Hat
Adiel's
Hat
Art's
Hat
Jerome's
Hat
Maurice's
Coat
Adiel's
Coat
Art's
Coat
Jerome's
Coat
Maurice
                 
Adiel
                 
Art
     
X
  X      
Jerome
                 

This means that Adiel took Art's hat (because the others are already accounted for, except his own), so he didn't take Art's coat, so he took Jerome's.  We check and red the appropriate boxes.
 

Maurice's
Hat
Adiel's
Hat
Art's
Hat
Jerome's
Hat
Maurice's
Coat
Adiel's
Coat
Art's
Coat
Jerome's
Coat
Maurice
                 
Adiel
    X           X
Art
     
X
  X      
Jerome
                 

This leaves only Adiel's hat for Maurice, so Jerome took Maurice's hat.  Maurice took Adiel's hat, so he didn't take Adiel's coat, so he took Art's coat (the only one left for him).  That means that Jerome took Adiel's coat, since it's the only one left for him.  Go ahead and check and red those boxes.
 

Maurice's
Hat
Adiel's
Hat
Art's
Hat
Jerome's
Hat
Maurice's
Coat
Adiel's
Coat
Art's
Coat
Jerome's
Coat
Maurice
 
X
          X  
Adiel
    X           X
Art
     
X
  X      
Jerome
X           X    

See how simple that was?  Aren't you glad you went through this exercise?

Last Update: 30 September 2003