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KCC's Quizzes AQQ292 about weighing using 2-plates scale

		
	
				

			

									
					    KCC
					
							

            
            			
				
									
											
			
			
				
  •  Analog Employees  

			
			
			    	
			                    
                
				                on Sep 30, 2025 
				
			
			
		

		
		                     
				
        		

		    
		    		    
		    			

			    
1. First, the quote of the week: "Some people create their own storms and then get mad when it rains" - Unknown


                                              




 2. New challenge with AQQ292 about using a two-plates scale.


This is a kind proposal from a frequent participant: Herman Neufeld, Analog & Mixed Signals Specialist):


  


You are asked to design a two-dish scale that weighs amounts of a substance from 1 to 40 grams in integer amounts.


Hence your task is to determine:


    

  1. What is the minimum number counterweights you need?
    2. 

  2. What are the weigh values of these counterweights?
    3. 



These, in order to weigh this substance,




Good luck and try to be among the first ones!


P.S. Please forward such quizzes to friends and colleagues who want also to "relax" their brains...

			

			
									
		                             
                        

    

                                            
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    •  Analog Employees  
    
            
						
                            
            
            				
            
                on Oct 1, 2025 6:24 AM
            
            
						
			            		
    
		
								
	
    

		
		
    
		
    
                                
                                                            
    
					
    Mag Concept: Balanced Ternary System
    

    In a two-dish scale, you can place counterweights on both sides of the scale. This allows you to simulate subtraction as well as addition. So instead of just summing weights, you can balance them by placing some on the same side as the substance and some on the opposite side.
    

    Balanced ternary uses digits:
    

      

    • −1 (weight on the same side as the substance)
      • 

    • 0 (weight not used)
      • 

    • +1 (weight on the opposite side)
      • 

    

    This system allows you to represent any integer using powers of 3.
    

    

    White check mark Solution
    

    a. Minimum number of counterweights needed:
    

    We need to find the smallest set of weights such that any integer from 1 to 40 can be represented using combinations of these weights on either side of the scale.
    

    Let’s use powers of 3:
    

    3^0=1,3^1=3,3^2=9,3^3=27,
    

    Now check the maximum representable value using balanced ternary with weights up to 3^3=27:
    

      

    • Maximum value =
       1+3+9+27=401
       (when all weights are placed on the opposite pan)
      • 

    

    So, 4 counterweights are sufficient.
    

    b. Weight values:
    

    The counterweights should be:
    

      

    • 1g
      • 

    • 3g
      • 

    • 9g
      • 

    • 27g
      • 

    
			
    

		
			
	      

		
		
	
    
	
    
		
    
			
		
    
	
    
	
    
		
						
				
				
						
				
				
		
		
    
			
		
    
	
    

    

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  • 
	
    






    
	
    
		
    
							
					
    
		
    
		    
		    		    
			
				
									
							        
			
			
			
    •  Analog Employees  
    
            
						
                            
            
            				
            
                on Oct 1, 2025 6:24 AM
            
            
						
			            		
    
		
								
	
    

		
		
    
		
    
                                
                                                            
    
					
    Mag Concept: Balanced Ternary System
    

    In a two-dish scale, you can place counterweights on both sides of the scale. This allows you to simulate subtraction as well as addition. So instead of just summing weights, you can balance them by placing some on the same side as the substance and some on the opposite side.
    

    Balanced ternary uses digits:
    

      

    • −1 (weight on the same side as the substance)
      • 

    • 0 (weight not used)
      • 

    • +1 (weight on the opposite side)
      • 

    

    This system allows you to represent any integer using powers of 3.
    

    

    White check mark Solution
    

    a. Minimum number of counterweights needed:
    

    We need to find the smallest set of weights such that any integer from 1 to 40 can be represented using combinations of these weights on either side of the scale.
    

    Let’s use powers of 3:
    

    3^0=1,3^1=3,3^2=9,3^3=27,
    

    Now check the maximum representable value using balanced ternary with weights up to 3^3=27:
    

      

    • Maximum value =
       1+3+9+27=401
       (when all weights are placed on the opposite pan)
      • 

    

    So, 4 counterweights are sufficient.
    

    b. Weight values:
    

    The counterweights should be:
    

      

    • 1g
      • 

    • 3g
      • 

    • 9g
      • 

    • 27g
      • 

    
			
    

		
			
	      

		
		
	
    
	
    
		
    
			
		
    
	
    
	
    
		
						
				
				
						
				
				
		
		
    
			
		
    
	
    

    

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