Question

Find all possible values of the fraction below. (Assume different letters are different digits, and the same letters are the same digits.) (G*R*O*U*N*D)/(B*A*S*E)

Answer 1

there is one possible value: 0.

Explanation:

We have 10 different letters in this fraction {G,R,O,U,N,D,B,A,S,E} and only 10 different digits {0,1,2,3,4,5,6,7,8,9}. It means that some letter must be equal to 0. Consider two cases:

I case:

`0 \in \{G, R, O, U, N, D\}`. Then enumerator of fraction must be equal to zero (because product of numbers with zero among them always zero).

So
`(GROUND)/(BASE) = (0)/(BASE) = 0` in this case.

II case:

`0 \in \{B,A,S,E\}`. Then for the same reasons as in I case denominator of fraction is equal to zero. And we know that fraction

`(BASE)/(0)` is not well-defined.