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Find all possible values of X - advanced question

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by shankar.ashwin » Mon Jan 09, 2012 12:46 am
adgir wrote:
Find all possible values of X.
0 cannot be one of the digits because 9 2 digit integers cannot be formed.

leaving 0 out, we still have 9 digits and 9C3 = 84 possible 3 digit integers combinations

who in her/his sane mind would calculate that? :D
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by ronnie1985 » Mon Jan 09, 2012 12:56 am
XYZ is the no. , say.
Then 100X+10Y+Z = 3(X+Y+Z)+30(X+Y+Z) = 33(X+Y+Z)
Therefore, the no of integral solutions of the equation 23Y+32Z = 67,134,201,268,335,402,469,536,603.
Which can be obtained by getting the coeff of x^(RHS of Equation) in the product: (1+x^23+x^46+...)*(1+x^32+x^64+...)
Quite lengthy
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