@ 2571, I have suggested the formula based on your below lines

(an answer is provided by entering a 1 in the appropriate column) however what I am trying to work out is whether I can apply a formula to the cells to stop the user from entering another 1 in another column causing duplicate answers per question
I thought that the cell values will be marked with 1 only instead of any other characters.

If you are sure that the input values are only Numbers then use the below one
Formula: copy to clipboard 
=COUNT($A2:$E2)=1


If the input data is anything then
Formula: copy to clipboard 
=COUNTA($A2:$E2)=1