On 05/06/2015 22:59, Johnny B Good wrote:

I'd say that 'guessing' likely values for n in this case (integer values
only) would be considered an entirely legitimate approach to take in
order to determine the value of n which can be the only value that also
allows the stated one in three probability to be true.

Yup, just call it "numerical analysis" or "stepwise refinement" ;-)

I'm sure there must be a more strict formula involving the use of square
roots but, since the algorithm for calculating a square root also
involves the use of 'guessed' values in an iterative process to swiftly
calculate a value of sufficient accuracy, I think the guessing method is
still entirely legitimate nonetheless. :-)

It is, in the sense that the expression quoted is quadratic, and
iterative methods like Newton-Raphson are valid techniques (made all the
more attractive by the advent of brute force computing power).

Having said that, the normal quadratic formula would work as well

0 = 1 +/- sqrt( 1 - (4 x -90) ) / 2

which gives roots of -9 and 10.


--
Cheers,

John.

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