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					    ambugua
					
							

            
            			
				
									
											
			
			
				
  •  Analog Employees  

			
			
			    	
			                    
                
				                on Mar 4, 2026 
				
			
			
		

		
		                     
				
        		

		    
		    		    
		    			

			    

By Kuo-Chang


math quiz



A checkerboard made as a 7 x 7 matrix has a green basic cell placed in its middle as shown in the above structure.


Questions:


    

  1. How many squares, defined in that matrix, are covering the green cell?
    2. 

  2. Can you extend the problem to any matrix size (i.e., n * n with n odd)? For example, what would be the answer for a 99 * 99 matrix?
    3. 







			

			
									    

			        
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[edited by: ambugua at 3:20 PM (GMT -4) on 9 Mar 2026]
				

						
		                             
                        
		


				
				        
        		

			
						
									
												
			
			
                        
                                    
                        
                        
                        
            
			            
						
						
			
			
			
			
		


        
         

    

    
        
    
            
                

            

               

                    
                        
                        
                    
               
 
               
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                on Jun 5, 2026 6:24 AM
            
            
						
			            		
    
		
								
	
    

		
		
    
		
    
                                
                                                            
    
					
    1. For the 7x7 matrix there are
         - 1 with size 1x1
         - 4 with size 2x2
         - 9 with size 3x3
         - 16 with size 4x4
         - 9 with size 5x5
         - 4 with size 6x6
         - 1 with size 7x7

       Total = 44 squares

    2. ... answer will follow...
    
			
    

		
			
	      

		
		
	
    
	
    
		
    
			
		
    
	
    
	
    
		
						
				
				
						
				
				
		
		
    
			
		
    
	
    

    

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                on Jun 6, 2026 6:29 PM
            
            
												
						in reply to RolandSa
					
										
			            		
    
		
								
	
    

		
		
    
		
    
                                
                                                            
    
					
    2. Solved with Excel:
    Filled column A with odd numbers from 1 to 99.
    Entered 1 into cell B1
    Entered formula "=B1+((A2-1)/2)^2+((A2+1)/2)^2" into cell B2
    Dragged down this formula all the way down to cell 50 which contains 99
    There you find the corresponding result = 83350

     

    
			
    

		
			
	      

		
		
	
    
	
    
		
    
			
		
    
	
    
	
    
		
						
				
				
						
				
				
		
		
    
			
		
    
	
    

    

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                on Jun 6, 2026 6:29 PM
            
            
												
						in reply to RolandSa
					
										
			            		
    
		
								
	
    

		
		
    
		
    
                                
                                                            
    
					
    2. Solved with Excel:
    Filled column A with odd numbers from 1 to 99.
    Entered 1 into cell B1
    Entered formula "=B1+((A2-1)/2)^2+((A2+1)/2)^2" into cell B2
    Dragged down this formula all the way down to cell 50 which contains 99
    There you find the corresponding result = 83350

     

    
			
    

		
			
	      

		
		
	
    
	
    
		
    
			
		
    
	
    
	
    
		
						
				
				
						
				
				
		
		
    
			
		
    
	
    

    

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