A 'Mean' Problem to Ponder

It's that time of year folks! Here's a problem for you or your students to think about as a warm-up for this week or for the SATs or for just developing logical thinking. It might also deepen student thinking about the distribution of data. You might find this question trivial but don't be too quick to judge this until your students try it! I would allow a calculator to be used. Observe how students approach this: Guess-Test, consideration of the 'mean', etc...

In a certain high school election, there were 12 candidates for President of the Student Council. If 1600 votes were cast and Denise received more votes than any of the others (i.e., she received a plurality), what is the least number of votes she could have received?