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HOW TO SOLVE 2 DIMENSIONAL LOGIC PROBLEMS

 A young woman went to a party, where she met Mr. Brown, Mr. White, Mr. Black, and Mr. Green. But she had too much to drink and later could only remember that they were a photographer, grocer, banker, and singer, in no particular order.

The hostess gave her 4 clues:
1.Mr. White approached the banker for a loan.
2.Brown had hired the photographer to take pictures of his wedding
3.White and the singer were friends, but never had any business dealings.
4.Neither Black nor the singer had ever met Green before this evening.

Who is who?

This is a two-dimensional problem, so named because there are two categories of information: names, and professions.

So, set up a 2 dimensional matrix, in the form of a table using the names as column headers, and professions as row headers. In the resultant cells of the table, put an 'X' to show an impossibility, and an 'O' to show a fact.

Here we show the table, and cells filled out with superscripts to show the rule number:

 Black
Brown
GreenWhite
banker
   X1
grocer
    
photographer
 X2
  
singer
X4
 X4
X3

5.Now since we know that the singer is NOT Black, Green, or White, it must be Brown. Put an 'O' in the Brown/singer cell, which means 'X' elsewhere for Brown:

 Black
Brown
Green
White
banker
 X5
 X1
grocer
 X5
  
photographer
 X2
  
singer
X4
O5
X4
X3

6.Now re-read the clues armed with the information from the new deduction: Brown is the singer and has done business with the photographer, but the singer has not done business with White (#3), or with Green(#4). Therefore Neither White, not Green can be the photographer. Now add the additional 'X's.

 Black
Brown
Green
White
banker
 X5 X1
grocer X5  
photographer
 X2X6
X6
singer
X4O5X4X3

7.And the additional facts implied by those 'X's

 Black
Brown
Green
White
banker
 X5 X1
grocer
 X5 O7
photographer
O7
X2X6X6
singer
X4O5X4X3

8.Now use the resultant Black and grocer 'O's to add new 'X's:

 Black
Brown
Green
White
banker
X8
X5 X1
grocer
X8
X5X8
O7
photographer
O7X2X6X6
singer
X4O5X4X3

 Since the only box open is the Green/banker one, the only possibility is that Green is the banker!

Copyright © 2001 by Paladin Consultants,LLC
Chatham, NJ
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This page revised   October 19, 2004