THE SOLUTION:

Jim used the felt pen to vote for Mim.
Kim used the crayon to vote for herself.
Mim used the ballpoint to vote for Vim.
Tim used the pencil to vote for Jim.
Vim used the highlighter to vote for Tim.

Oh, and Kim won the position. The salespeople all knew that the “promotion” meant longer hours at the office and fewer opportunities to get out there and sell (and make the big bucks). Harry quickly determined that anyone who voted for him/herself deserved the position, since (1) it exhibited confidence in that person’s ability, and (2) it must have been cast by a person who really wanted the job.

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