HOW TO SOLVE 3 DIMENSIONAL LOGIC PROBLEMS
Andy, Chris, Noel, Randy and Steve were all recently hired as stand vendors at Yankee stadium. One of their last names is Morse, and each sells only one product.
1.Randy, whose last name is not Wiley sells no popcorn.
2.The Davis boy does not sell soda or candy.
3.The five boys are Noel, Randy, the Smith boy, the Cobble boy, and the ice cream seller.
4.Andy's last name is not Wiley or Cobble, and neither Andy nor the Cobble boy sell candy.
5.Neither Steve nor Davis sell peanuts or ice cream.
What are the full names of the boys, and what does each of them sell?
This is called a 3 dimensional problem because of the 3 categories: first names, last names, and product sold.
To solve this type of problem, you need a 3 dimensional table. The representation is difficult on a 2 dimensional surface like this document, but you can visualize that the first names relate to product, the last names relate to product, and the first and last names relate to each other. Draw the matrix like this:
Now go through the clues placing an 'X' in cells to indicate an elimination, , and an 'O' to indicate a fact. We've gone through the 5 clues and places the X's and O's in the appropriate cell, and annotated then with footnotes corresponding to the clue #s.
6.Now using deductive reasoning, you know that the Davis boy must sell popcorn. Put an 'O' in the Davis/popcorn cell, and fill in the rest of the lastname/popcorn cells with 'X's.
7. And since Randy doesn't sell popcorn, his name can't be Davis. Therefore it must be Morse. Fill in the 'X' in the Randy/Davis cell, implying an 'O' in the Randy/Morse cell.
8.Since Randy's last name is Morse, now you can take the Randy facts and transfer them to Morse, viz Morse does not sell icecream
9.Now it is apparent that Wiley sells icecream. Put an 'O' in Wiley icecream, and 'X's for the other Wiley Products.
10.Using the icecream information, you now know that Noel, Randy and Steve cannot be named Wiley, because these three boys do not sell icecream.. Enter the 'X's. We already know from #5 that Randy's last name is not Wiley
11.Now we conclude that Chris's last name is Wiley, that Chris sells Ice cream (because Wiley does), and not Cobble, Davis, or Morse or Smith. They're falling like dominoes now!
12. We also know that Andy doesn't sell ice cream (because Chris Wiley does), that Steve's name is Cobble, and no one else's is.
13.Now transfer to Steve what you know about Cobble, and to Cobble what you know about Steve
14. So Cobble sells soda, therefore Steve sells soda. Therefore Andy, Chris Noel, Randy, Morse and Smith do not sell soda. Fill in the 'O's and 'X's
15. By elimination, Smith must be Andy's last name. Therefore Smith sells no candy. Therefore he must sell peanuts. That means that Morse sells candy, and so does Randy.
By elimination, the answer is