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Cell protection is active for all cells by default. If only certain cells are to be protected, this setting must be turned off.

Select the entire spreadsheet. (A quick way is to click the little gray box above row 1 and to the left of column A.)
From the pull-down menus, select Format > Cells.
In the dialog that appears, select the Cell Protection tab.
Uncheck the box next to Protected to remove the protection on all cells.

To select a range of cells to protect, or to select non-adjacent cells to protect:

Hold down the Ctrl key while clicking on the non-adjacent cells to highlight the ones that are to be protected.
When all of the desired cells are selected, in the pull-down menus, go to Format > Cells...
In the dialog that appears, select the Cell Protection tab.
Click on the box next to Protect.
Click OK.

Once the cells are marked for protection, the protection option must be enabled at the sheet or spreadsheet level:

From the pull-down menus, select Tools > Protect Document > Sheet or Tools > Protect Document > Document.
In the dialog that appears, provide a password , then confirm it by typing it again.
Click OK.
The protected cells will now be uneditable.