[Nottingham] A numerical puzzle & "mathomatic"

[Martin]

Folks,

Playing with what should be a simple numerical puzzle, I've discovered
three things...

My algebra skills are a little rusty;

"Mathomatic" is rather a neat little mathematics tool:
http://mathomatic.org
(Now why didn't I know about that when struggling with Laplace
transforms?!!!)

And other than to use "brute force", the simple puzzle is rather puzzling!


The puzzle is:

(a + b + c)^2 + (a + b + c) = 100*a + 10*b + c

where 0 <= a <= 9, 0 <= b <= 9, 0 <= c <= 9. That is, a, b, c are single
digit integers. "abc" forms a 3 digit number.

The answer is very easily found by brute force.


More interestingly, anyone up for showing the algebraic solution?

Or is it really just a case of plotting a 3d graph of:

0 = (a*(99 - a - (2*(b + c)))) + (b*(9 - b - (2*c))) - (c^2)

to find the zero crossing point?


Cheers,
Martin

-- 
----------------
Martin Lomas
martin at ml1.co.uk
----------------