There are
real numbers,
, with the property that whenever one of them is removed, the remaining
can be split into two sets of
elements each so that both sets have the same sum. Prove that all the numbers are equal.
Attached is a solution to this balancing problem that is readable in
Wordpad but not when pasted into this chatting space. The formatting looks bad in MS Word also, so please use
Wordpad to open this file. The topic may be almost two years old, but the problem is still worth focused attention by any curious math student, in that it stimulates explorations in unfamiliar territory. Cheers!
![\Large\hspace{5}\unitlength{1} \picture(175,100){~(50,50){\circle(100)} (1,50){\overbrace{\line(46)}^{4$\;\;a}} (52,50){\line(125)}~(50,52;115;2){\mid}~(52,55){\longleftar[60]} (130,56){\longrightar[35]}~(116,58){r}~(c85,50;80;2){\bullet} (c85,36){3$-q}~(c165,36){3$q} (42,29){\underbrace{\line(32)}_{1$a^2/r\;\;\;}}~}](http://www.vesco.us/forums/Sources/latex/pictures/7027a1b6e73c275fda1cf7e68eca2df1.gif "\Large\hspace{5}\unitlength{1} \picture(175,100){~(50,50){\circle(100)} (1,50){\overbrace{\line(46)}^{4$\;\;a}} (52,50){\line(125)}~(50,52;115;2){\mid}~(52,55){\longleftar[60]} (130,56){\longrightar[35]}~(116,58){r}~(c85,50;80;2){\bullet} (c85,36){3$-q}~(c165,36){3$q} (42,29){\underbrace{\line(32)}_{1$a^2/r\;\;\;}}~}")
