[If you are looking here from *The Omega* (Thompson Rivers University’s student newspaper) where these puzzles are also published, you may be wondering why this puzzle is different. I screwed up. When finalising my solution write-up, I realised that I had failed to follow one of the constraints. Enjoy the extra puzzle.]

The sum of two six-sided dice rolled together is used in many games for moves. Some games use other die roll combinations for various purposes. For many of these, it is fairly easy to figure out their distributions and averages. Some are a bit more difficult. Like this puzzle’s.

What is the average of best three out of four six-sided dice rolled together? (Roll four six-sided dice and take the sum of the three highest dice. If there is a tie for lowest value, just disregard only one of the dice.)

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. **The deadline is Wednesday, November 25, 2015 at noon Pacific Time.** I will post the answer shortly after.