Paladin Consultants, LLC

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:

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:

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.

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

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

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

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