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?