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	Green	White
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		X2	X6	X6
singer	X4	O5	X4	X3

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

	Black	Brown	Green	White
banker		X5		X1
grocer		X5		O7
photographer	O7	X2	X6	X6
singer	X4	O5	X4	X3

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	X5	X8	O7
photographer	O7	X2	X6	X6
singer	X4	O5	X4	X3

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 All Rights Reserved This page revised   October 19, 2004