Puzzle on 3/1/03
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Sue, Sally, Bobby, and Billy are
9, 11, 13, and 14 years old.

Bobby is older than Billy and younger than Sue.

Sally is younger than Bobby and older than Billy.

How old is each person?

The solution

 

Let's make a table and record what we know from the clues.

 
9
11
13
14
Sue        
Sally        
Bobby        
Billy        

 
Bobby is older than Billy (FIRST CLUE).
9
11
13
14
Sue        
Sally        
Bobby
NO
    
 
Billy      
NO
Bobby is younger than Sue (ALSO FIRST CLUE).
9
11
13
14
Sue
NO
      
Sally        
Bobby
NO
    
NO
Billy      
NO
 
Sally is younger than Bobby (SECOND CLUE).
9
11
13
14
Sue
NO
      
Sally
NO
      
Bobby
NO
NO
  
NO
Billy      
NO
So Bobby is the 14 (and we know who else isn't 14).
9
11
13
14
Sue
NO
  
NO
  
Sally
NO
  
NO
  
Bobby
NO
NO
YES
NO
Billy
 
 
NO
NO
Sue is older than Bobby (BACK TO CLUE 1), and Sally is not 15.
9
11
13
14
Sue
NO
NO
NO
YES
Sally
NO
  
NO
NO
Bobby
NO
NO
YES
NO
Billy
 
 
NO
NO
That leave Sally as 11. and Billy isn't 11.
9
11
13
14
Sue
NO
NO
NO
YES
Sally
NO
YES
NO
NO
Bobby
NO
NO
YES
NO
Billy
 
NO
NO
NO
 
All that is left is to put Billy in the chart.
9
11
13
14
Sue
NO
NO
NO
YES
Sally
NO
YES
NO
NO
Bobby
NO
NO
YES
NO
Billy
YES
NO
NO
NO
 

Billy is 9, Sally is 11, Bobby is 13, and Sue is 14.
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