Quote:
Originally Posted by issybird
N/2 X (1+N)
Can't prove it, though.
(I had my own Gaussian moment in school, but it was later than the third grade)
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Yes!
Quote:
Originally Posted by pdurrant
Write out all the numbers 1...N in order. Write them all out in reverse order. Ann the rows together. Obviously the total of each colum is (N+1) and the full total is Nx(N+1). But we want half that. N/2x(N+1). Issybird has the right answer.
Code:
1 2 3 .... (N-2) (N-1) N
N (N-1) (N-2) .... 3 2 1
========================================
(N+1) (N+1) (N+1) .... (N+1) (N+1) (N+1)
HTH |
Well done. I would have also accepted a proof by
Mathematical Induction. Your derivation and proof was supposedly the one offered by a very young Gauss. For that alone I guess it would rate as being more elegant.
So I would say either Issybird or Pdurrant should offer the next question, whoever does so first.