Magical Numbers!

Number Theory Level pending

Let's define 'Magical Number' !

A Magical Number P is a decimal number consisting of 2n digits with the properties that

(I) No digit of P is 0 (Zero);

(II) Sum of the digits of P is equal to A and

(III) Product of the digits of P equals B,


and n is a natural number.

For example, for P=1236 with A=12 and B=36, Sum of Digits of P=1+2+3+6=12=A and Product of digits of P=1×2×3×6=36=B . Yeah, 1236 is a Magical Number.

You have to find out the number of Magical numbers greater than 1236 and less than 1 Billion.


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