Quadruple Pentominoes

Introduction

Livio Zucca's Triple Pentominoes studies the problem of finding a compatibility figure for three pentominoes. This problem is quite hard.

In 2013 he proposed to me the same problem for four pentominoes. This problem is even harder! Here are the smallest known solutions. If you find a smaller solution or solve an unsolved case, please write.

Solutions

Cases that include 5I-5X, 5U-5X, 5V-5X, 5W-5X, or 5X-5Z are impossible. They do not appear in the table below.

If a cell is shaded, one or more of the corresponding triples is unsolved.

5F-5I-5L-5N5F-5I-5L-5P5F-5I-5L-5T5F-5I-5L-5U5F-5I-5L-5V
 
5F-5I-5L-5W5F-5I-5L-5Y5F-5I-5L-5Z5F-5I-5N-5P5F-5I-5N-5T5F-5I-5N-5U
   
5F-5I-5N-5V5F-5I-5N-5W5F-5I-5N-5Y5F-5I-5N-5Z
 
5F-5I-5P-5T5F-5I-5P-5U5F-5I-5P-5V5F-5I-5P-5W5F-5I-5P-5Y
 
5F-5I-5P-5Z5F-5I-5T-5U5F-5I-5T-5V5F-5I-5T-5W5F-5I-5T-5Y
    
5F-5I-5T-5Z5F-5I-5U-5V5F-5I-5U-5W5F-5I-5U-5Y5F-5I-5U-5Z5F-5I-5V-5W
     
5F-5I-5V-5Y5F-5I-5V-5Z5F-5I-5W-5Y5F-5I-5W-5Z
  
5F-5I-5Y-5Z5F-5L-5N-5P5F-5L-5N-5T5F-5L-5N-5U5F-5L-5N-5V
 
5F-5L-5N-5W5F-5L-5N-5X5F-5L-5N-5Y5F-5L-5N-5Z5F-5L-5P-5T5F-5L-5P-5U
 
5F-5L-5P-5V5F-5L-5P-5W5F-5L-5P-5X5F-5L-5P-5Y5F-5L-5P-5Z
5F-5L-5T-5U5F-5L-5T-5V5F-5L-5T-5W5F-5L-5T-5X5F-5L-5T-5Y
 

Livio Zucca

 
5F-5L-5T-5Z5F-5L-5U-5V5F-5L-5U-5W5F-5L-5U-5Y5F-5L-5U-5Z5F-5L-5V-5W
    
5F-5L-5V-5Y5F-5L-5V-5Z5F-5L-5W-5Y5F-5L-5W-5Z5F-5L-5X-5Y
 
5F-5L-5Y-5Z5F-5N-5P-5T5F-5N-5P-5U5F-5N-5P-5V5F-5N-5P-5W5F-5N-5P-5X
5F-5N-5P-5Y5F-5N-5P-5Z5F-5N-5T-5U5F-5N-5T-5V5F-5N-5T-5W5F-5N-5T-5X
   
5F-5N-5T-5Y5F-5N-5T-5Z5F-5N-5U-5V5F-5N-5U-5W5F-5N-5U-5Y
  
5F-5N-5U-5Z5F-5N-5V-5W5F-5N-5V-5Y5F-5N-5V-5Z
 

Livio Zucca

5F-5N-5W-5Y5F-5N-5W-5Z5F-5N-5X-5Y5F-5N-5Y-5Z
5F-5P-5T-5U5F-5P-5T-5V5F-5P-5T-5W5F-5P-5T-5X5F-5P-5T-5Y
 
5F-5P-5T-5Z5F-5P-5U-5V5F-5P-5U-5W5F-5P-5U-5Y5F-5P-5U-5Z5F-5P-5V-5W
    
5F-5P-5V-5Y5F-5P-5V-5Z5F-5P-5W-5Y5F-5P-5W-5Z5F-5P-5X-5Y5F-5P-5Y-5Z

Livio Zucca

 
5F-5T-5U-5V5F-5T-5U-5W5F-5T-5U-5Y5F-5T-5U-5Z5F-5T-5V-5W5F-5T-5V-5Y
     
5F-5T-5V-5Z5F-5T-5W-5Y5F-5T-5W-5Z5F-5T-5X-5Y5F-5T-5Y-5Z5F-5U-5V-5W
     
5F-5U-5V-5Y5F-5U-5V-5Z5F-5U-5W-5Y5F-5U-5W-5Z5F-5U-5Y-5Z5F-5V-5W-5Y
     
5F-5V-5W-5Z5F-5V-5Y-5Z5F-5W-5Y-5Z5I-5L-5N-5P5I-5L-5N-5T
  

Gabriele Carelli

 
5I-5L-5N-5U5I-5L-5N-5V5I-5L-5N-5W5I-5L-5N-5Y
 

Livio Zucca

5I-5L-5N-5Z5I-5L-5P-5T5I-5L-5P-5U5I-5L-5P-5V
  
5I-5L-5P-5W5I-5L-5P-5Y5I-5L-5P-5Z5I-5L-5T-5U5I-5L-5T-5V

Livio Zucca

   
5I-5L-5T-5W5I-5L-5T-5Y5I-5L-5T-5Z5I-5L-5U-5V5I-5L-5U-5W5I-5L-5U-5Y
     
5I-5L-5U-5Z5I-5L-5V-5W5I-5L-5V-5Y5I-5L-5V-5Z5I-5L-5W-5Y
 

Livio Zucca

 
5I-5L-5W-5Z5I-5L-5Y-5Z5I-5N-5P-5T5I-5N-5P-5U5I-5N-5P-5V
   

Livio Zucca

5I-5N-5P-5W5I-5N-5P-5Y5I-5N-5P-5Z5I-5N-5T-5U5I-5N-5T-5V

Livio Zucca

  
5I-5N-5T-5W5I-5N-5T-5Y5I-5N-5T-5Z5I-5N-5U-5V5I-5N-5U-5W5I-5N-5U-5Y
    
5I-5N-5U-5Z5I-5N-5V-5W5I-5N-5V-5Y5I-5N-5V-5Z
  
5I-5N-5W-5Y5I-5N-5W-5Z5I-5N-5Y-5Z5I-5P-5T-5U5I-5P-5T-5V
    
5I-5P-5T-5W5I-5P-5T-5Y5I-5P-5T-5Z5I-5P-5U-5V5I-5P-5U-5W
    
5I-5P-5U-5Y5I-5P-5U-5Z5I-5P-5V-5W5I-5P-5V-5Y5I-5P-5V-5Z
   
5I-5P-5W-5Y5I-5P-5W-5Z5I-5P-5Y-5Z5I-5T-5U-5V5I-5T-5U-5W
    
5I-5T-5U-5Y5I-5T-5U-5Z5I-5T-5V-5W5I-5T-5V-5Y5I-5T-5V-5Z5I-5T-5W-5Y
      
5I-5T-5W-5Z5I-5T-5Y-5Z5I-5U-5V-5W5I-5U-5V-5Y5I-5U-5V-5Z5I-5U-5W-5Y
      
5I-5U-5W-5Z5I-5U-5Y-5Z5I-5V-5W-5Y5I-5V-5W-5Z5I-5V-5Y-5Z
    
5I-5W-5Y-5Z5L-5N-5P-5T5L-5N-5P-5U5L-5N-5P-5V5L-5N-5P-5W5L-5N-5P-5X
  
5L-5N-5P-5Y5L-5N-5P-5Z5L-5N-5T-5U5L-5N-5T-5V5L-5N-5T-5W
  
5L-5N-5T-5X5L-5N-5T-5Y5L-5N-5T-5Z5L-5N-5U-5V
  
5L-5N-5U-5W5L-5N-5U-5Y5L-5N-5U-5Z5L-5N-5V-5W
 
5L-5N-5V-5Y5L-5N-5V-5Z5L-5N-5W-5Y5L-5N-5W-5Z5L-5N-5X-5Y
  
5L-5N-5Y-5Z5L-5P-5T-5U5L-5P-5T-5V5L-5P-5T-5W
 
5L-5P-5T-5X5L-5P-5T-5Y5L-5P-5T-5Z5L-5P-5U-5V
 
5L-5P-5U-5W5L-5P-5U-5Y5L-5P-5U-5Z5L-5P-5V-5W5L-5P-5V-5Y
 
5L-5P-5V-5Z5L-5P-5W-5Y5L-5P-5W-5Z5L-5P-5X-5Y

Livio Zucca

5L-5P-5Y-5Z5L-5T-5U-5V5L-5T-5U-5W5L-5T-5U-5Y5L-5T-5U-5Z5L-5T-5V-5W
  

Gabriele Carelli

Gabriele Carelli

5L-5T-5V-5Y5L-5T-5V-5Z5L-5T-5W-5Y5L-5T-5W-5Z5L-5T-5X-5Y5L-5T-5Y-5Z
    
5L-5U-5V-5W5L-5U-5V-5Y5L-5U-5V-5Z5L-5U-5W-5Y
  
5L-5U-5W-5Z5L-5U-5Y-5Z5L-5V-5W-5Y5L-5V-5W-5Z5L-5V-5Y-5Z
 

Gabriele Carelli

  
5L-5W-5Y-5Z5N-5P-5T-5U5N-5P-5T-5V5N-5P-5T-5W5N-5P-5T-5X
  
5N-5P-5T-5Y5N-5P-5T-5Z5N-5P-5U-5V5N-5P-5U-5W
 
5N-5P-5U-5Y5N-5P-5U-5Z5N-5P-5V-5W5N-5P-5V-5Y
 
5N-5P-5V-5Z5N-5P-5W-5Y5N-5P-5W-5Z5N-5P-5X-5Y
 
5N-5P-5Y-5Z5N-5T-5U-5V5N-5T-5U-5W5N-5T-5U-5Y5N-5T-5U-5Z5N-5T-5V-5W
     
5N-5T-5V-5Y5N-5T-5V-5Z5N-5T-5W-5Y5N-5T-5W-5Z5N-5T-5X-5Y
   
5N-5T-5Y-5Z5N-5U-5V-5W5N-5U-5V-5Y5N-5U-5V-5Z5N-5U-5W-5Y
  
5N-5U-5W-5Z5N-5U-5Y-5Z5N-5V-5W-5Y5N-5V-5W-5Z5N-5V-5Y-5Z
    
5N-5W-5Y-5Z5P-5T-5U-5V5P-5T-5U-5W5P-5T-5U-5Y5P-5T-5U-5Z

Livio Zucca

    
5P-5T-5V-5W5P-5T-5V-5Y5P-5T-5V-5Z5P-5T-5W-5Y5P-5T-5W-5Z
   
5P-5T-5X-5Y5P-5T-5Y-5Z5P-5U-5V-5W5P-5U-5V-5Y
 
5P-5U-5V-5Z5P-5U-5W-5Y5P-5U-5W-5Z5P-5U-5Y-5Z5P-5V-5W-5Y
   
5P-5V-5W-5Z5P-5V-5Y-5Z5P-5W-5Y-5Z5T-5U-5V-5W5T-5U-5V-5Y
    
5T-5U-5V-5Z5T-5U-5W-5Y5T-5U-5W-5Z5T-5U-5Y-5Z5T-5V-5W-5Y5T-5V-5W-5Z
     
5T-5V-5Y-5Z5T-5W-5Y-5Z5U-5V-5W-5Y5U-5V-5W-5Z5U-5V-5Y-5Z
    
5U-5W-5Y-5Z5V-5W-5Y-5Z
  

Last revised 2014-11-11.

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Col. George Sicherman [ HOME | MAIL ]