By my simple Monte Carlo analysis, it seems that Puddles could do any number of pushups except for 1, 4, or 5. Any number 6 or above seems possible. There seem to be 79 different scoring permutations that would lead to 506 pushups with 23 unique total scores from that lot. The lowest score to yield 506 pushups is 53 points, the maximum score seems to be 82, and there are five ways to score 72 points with 506 pushups. A quick glance at the data doesn't reveal any obvious pattern to the last score for high-scoring games (50+ points). Kerry -- lkmitch@gmail.com www.kerrymitchellart.com http://spacefilling.blogspot.com/ On Mon, Nov 1, 2010 at 9:06 AM, Henry Baker <hbaker1@pipeline.com> wrote:
The U Oregon mascot "Puddles" Duck does k pushups after each time the Oregon football team scores, where k is the _total_ number of points scored in the game so far. (The "point(s)" after are included in the touchdown points, and aren't considered a separate score.) For example, in the recent Oregon-New Mexico game, Puddles did 506 pushups.
http://content.usatoday.com/communities/campusrivalry/post/2010/09/oregon-ma...
The Puddles Duck function PD(scores) associated with a sequence of football scores is the total number of pushups done in a game with that sequence of scores. For concreteness, use American football rules:
http://en.wikipedia.org/wiki/American_football_rules#Scoring
Questions about this function:
* Characterize the image set of this function -- finite or infinite (Oregon doesn't waste any time in huddles!)
* In how many ways can Puddles achieve n pushups?
* What can we tell about the scoring sequence, given the Puddles number? E.g., what can we tell about the number of touchdowns, numbers of field goals, extra points, etc., just from knowing that Puddles did 506 pushups? On a sufficiently high scoring game, can we tell what the last score was (touchdown/touchdown+1/touchdown+2/...)?
Where is that Gauss child when we need him?
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