Implement my method of adding numbers mentally
Ruby, 148 144 142 bytes

f=-&gt;a{a.sort!
(a.size/2).times{a[~-$.+=2,0]=a.pop}
a*="  "
puts$`+$&amp;+$'while a.gsub!(/\d+\s+\d+/){"#{eval$&amp;.split*?+}".ljust$&amp;.size}
puts'',a}


So disappointingly long... To run:

f[ [314,495,767,214,141] ]


Prints:

141  767  214  495  314
908       709       314
1617                314

1931