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I know that I can select individual evaluatable cells and disable their Open property (through Cell > Cell Properties), but is there a simple way to toggle the Open status of all evaluatable cells?

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Something like this? (V9 and after only, because of Cells.)

toggleCellOpen[nb_: SelectedNotebook[]] :=
 (CurrentValue[#, CellOpen] = Not@CurrentValue[#, CellOpen]) & /@ 
   Select[Cells[], CurrentValue[#, Evaluatable] &]
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