The Math Factor Podcast

I had a dream last night involving — (?) well I am not really sure, except that it left me wondering if there is a simple proof (if indeed it is true) that there must be a common factor of

m choose i = m!/(i! (m-i)!)
m choose j = m!/(j! (m-j)!)

for all counting numbers i,j,m with 1 < i,j < m

Another way to state this same thing is: any pair of entries, on any row of Pascal’s triangle (except for the 1’s on the edges) will have a common factor.

With facts of this sort, often there is a clever way to cast things in terms of counting something a couple of different ways which makes things clear.

Peter Winkler tell us which full house to choose, and asks: How long must we wait until all the ants fall off the rod?

 

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Peter Winkler brings us a short poker puzzle, from his new collection Mathematical Mind Benders: What is the best full house?

(The answer is not three aces and two kings…)

 

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Robert Schneider, of The Apples In Stereo discusses his logarithmic tonal system and why he loves mathematics.

 

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Prof. Bernie Madison discusses his innovative course at the University of Arkansas; thinking straight about mathematics is fundamental for an informed and capable citizenry– but why doesn’t mathematics education seem to foster this?

 

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