13. In the expression $\frac{\text { k.a.n.g.a.r.o.o }}{\text { g.a.m.e }}$, different letters stand for different non-zero digits but the same letter always stands for the same digit. What is the smallest possible integer value of the expression?
13. 002 The expression may be simplified to $\frac{k \cdot a \cdot n \cdot r \cdot o \cdot o}{m \cdot e}$.
The smallest possible numerator is $5 \times 4 \times 3 \times 2 \times 1 \times 1=120$.
The largest possible denominator is $9 \times 8=72$.
The smallest possible value of the expression, whether integer or not, is therefore $\frac{120}{72}=1 \frac{2}{3}$.
We may obtain a value of 2 for the expression via $\frac{6 \times 4 \times 3 \times 2 \times 1}{9 \times 8}$.
Therefore the smallest possible integer value of the expression is 2 .