Everybody knows that you can pick your Humanatone among 8 colors : red, orange, yellow, green, blue, violet plus pink and bordeaux/purple.
But how many different colors for the german plastic Nasenflöte ? I do not know which is the maker (if someone knows it, please let me know!). It is mainly distributed by Gewa and Arnold Stölzel, and wear a swan as a logo :
So, how many colors for the "swan" nose flute ? These Nasenpfeifen are two colored. And there are 13 different colors : white, yellow, orange, red, bordeaux, purple, violet, blue, green plus 4 scarcer colors : pastel blue, pink, silver and gold.
The trick is that no swan flute has got its two parts by the same color.
The answer is (n x n) - n.
(13 x 13) - 13 gives the choice between 156 different flutes to the public !
Oh! For sure, with online shops, you are never able to choose the color...They generally say "Assorted colors, sorry, no choice".
So, how many flutes in average a compulsive collector has to buy to get the complete collection (according to a homogeneous distribution of colors...)?
The answer is n x ( Ln(n) + γ) where γ is the Euler-Mascheroni constant (~0,577).
That is 878 swan nose flutes !
Very interesting post, isn't it ?