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This nonogram should require at least 2 guesses, no matter where you put them:

     1 1 1   
     1 1 1 2 1
   2 . . . . .
   2 . . . . .
  11 . . . . .
  11 . . . . .
   1 . . . . .


That puzzle has two solutions no?

     1 1 1   
     1 1 1 2 1
   2 x x . . .
   2 . . x x .
  11 x . . x .
  11 . x . . x
   1 . . x . .
and

     1 1 1   
     1 1 1 2 1
   2 x x . . .
   2 . . x x .
  11 . x . x .
  11 x . . . x
   1 . . x . .
(found these with an SMT solver :D)




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