November 2010 - mathfun@mailman.xmission.com

[math-fun] U Oregon "Puddles" Duck sequence
by Henry Baker 02 Nov '10

02 Nov '10

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-m… 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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[math-fun] a question of sand
by Simon Plouffe 01 Nov '10

01 Nov '10

Hello , I read recently that the calculated the approx. amount of stars in the known universe to be 7x10^22, which is according to source, greater than the number of grains of sand in all the deserts and beaches on earth. Well, this is quite big, but as I was explaining this to some people around me, is there a known value of the number of grains of sand in let's say 1 cubic meter of sand ? I know some are very small and others are bigger : does someone has an approximate value ? I tried to find without success and also I have no idea on how to calculate this simple value. Thanks for any answer(!). source : a certain australian study : http://en.wikipedia.org/wiki/Observable_universe best regards and have a nice evening. Simon Plouffe

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[math-fun] for anyone who enjoys collaborative problem-solving
by Gary Antonick 01 Nov '10

01 Nov '10

Hi math-fun group, If you enjoy collaborative problem-solving consider trying this week's logic puzzle in the NTY crossword blog. (I wrote the post.) Goal of the post is not so much to solve the puzzle as to explore it. Would be great to get some math-fun participants in the mix. Here's the puzzle: can you insert several pluses between the digits 987654321 to make an expression equal to 99? http://wordplay.blogs.nytimes.com/2010/11/01/numberplay-sum-fun/ The puzzle is easy but I think may give rise to some interesting discussion this week: eg could 98765432 also make 99? What about 9876543? What's the smallest number these could make? Second-smallest? etc. - Gary PS- I hesitated to send the group a link to an outside discussion but hope this one is worth it.

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Re: [math-fun] U Oregon "Puddles" Duck sequence
by Henry Baker 01 Nov '10

01 Nov '10

Oops, I meant the number of non-representable numbers, finite or infinite. At 09:06 AM 11/1/2010, Henry Baker wrote: >* Characterize the image set of this function -- finite or infinite (Oregon doesn't waste any time in huddles!)

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