### puzzle answer: avg(sums(a set))

This is the answer to the last math puzzle. You should check out the puzzle before you read the answer!

It turns out that

avg(sums(

Why?

The main observation is that, for any

It turns out that

avg(sums(

*S*)) = ½ ∑S.Why?

The main observation is that, for any

*T*⊂*S*, avg({∑*T*, ∑(*S-T*)}) = ½ ∑*S*. We should also note that if ∑*T*= ∑_{1}*T*, then ∑_{2}*S-T*= ∑_{1}*S-T*; this means that whenever the sums of_{2}*T*and_{1}*T*overlap in sums(_{2}*S*), so do the sums of their complements. If we think of adding each pair {∑*T*, ∑(*S-T*)} one at a time to build sums(*S*), then either both elements of the pair are already in the set, or both are not -- either way, the average remains the same.
## 1 Comments:

[url=http://www.pinskerdream.com/bloghoster/?u=videosealton6]Internet TV and Radio Player 4.0[/url] [url=http://www.answerbag.com/profile/1238305]Fantasy DVD Player Platinum 9.4.3[/url]

MediaChance DVD-lab Pro 2.5 Dub2DV

http://www.adulthostedblogs.com/?u=videoseashley2 DivX ProDivX Player 6.7.0.18

[url=http://www.answerbag.com/profile/1237055]Power DVD Player 7[/url] [url=http://www.drawingboard.org/blogs/?u=videoseabby8]A-Z Video Converter Ultimate 7.51[/url]

FreeStar Free Video Converter Aone Ultra Flash Video FLV Converter 3.8.1023

http://www.drawingboard.org/blogs/?u=videosealton8 DVD-lab 1.3.1 Standard

ConvertX to DVD 2.99.13.970

my icq:858499940385

Post a Comment

<< Home