Check a collection if it contains all the values that match a certain value
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My question might sound naive. Please excuse me for that.
I want to know what is the best way to know if a collection has all values that match a certain value. Or in simple words, all values in a collection match a unique value. 

    *List<Integer> listOfStrings = new ArrayList<Integer>();*

All I want to know is if all the entries in the "listOfStrings" match a certain value, lets say 1.

Apologies again for a naive question but I need the fastest way. I have a solution with me but that is very rudimentary.

Regards