head-scratch·ing
                    
                                                                                                              
                                                                                                                                  ˈhed-ˌskra-chiŋ  
                                                      
                                                          
            
        informal      
      
                                
                                
              
          
                                                      : the act or activity of scratching one's head while pondering or puzzling over something difficult to understand                                      
                
                  —used figuratively
Every year, around the middle of October, the finalists for the National Book Awards are announced to general bafflement. Specifically, it's the fiction shortlist that provokes head-scratching.— Laura Miller
Laura Miller
This is, ahem, a very complex scientific process involving a great deal of head-scratching and thoughtful staring.— Tom Jordan
Tom Jordan
    
                
                                
            also                
          
                                                      : confusion                                      
            
            
        informal      
      
                                
                                
              
          
                                                      : difficult to understand : causing puzzlement or confusion                                      
              
                             
… the system can lead to head-scratching results …— Mark Bechtel
Mark Bechtel
                                       … we'll be revisiting some of the best, worst, and most head-scratching moments from our archives.— Doug Brod
Doug Brod
                         
                
                    
                                                      head-scratchingly
                                      adverb
                                                                                                      
                        
                        
    
          
         
                        head-scratchingly poor decisions    
  
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  Merriam-Webster unabridged




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