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Solution to Puzzle 99.  Pizza Dinner

Jim, Kim, Larry, Minna, and Nancy had their pizza dinner at a restaurant.  Each of them had three toppings from among the following:  sausage, pepperoni, mushroom, olives, and green pepper.  

From the following information, we fill the table below with "Y" (for haves).

1) The only topping that Jim and Larry had in common was sausage.  

2) The only topping Larry and Kim had in common was mushroom.  

3) The only topping Kim and Minna had in common was green pepper.  

4) The only topping Minna and Nancy had in common was pepperoni.  

  sausage mushroom green pepper pepperoni olives
Jim Y        
Larry Y Y      
Kim   Y Y    
Minna     Y Y  
Nancy       Y  

We than fill out alternatively each cells in the able with Y (for yes) and N (for No) since we know that:

1) Except for sausage, Jim cannot have what other toppings Larry has.  

2) Except for mushroom, Larry cannot have what other toppings Kim has. 

3) Except for green pepper, Kim cannot have what other toppings Minna has.  

4) Except for pepperoni, Minna cannot have what other toppings Nancy has.  

  sausage mushroom green pepper pepperoni olives
Jim Y X Y X  
Larry Y Y X Y  
Kim X Y Y X  
Minna Y X Y Y  
Nancy X Y X Y  

Finally, the last column is filled out since we know each one of them has three toppings. 

 

  sausage mushroom green pepper pepperoni olives
Jim Y X Y X Y
Larry Y Y X Y X
Kim X Y Y X Y
Minna Y X Y Y X
Nancy X Y X Y Y

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