A player tossing a coin is to score one point for every head he turns up and two for every tail. He keeps on tossing the coin and writes a series formed by cumulative score after every toss. The chance that 100 will appear in the series is $\frac{1}{\mathrm{a}}\left\{\mathrm{b}+{\left(\frac{1}{\mathrm{b}}\right)}^{\mathrm{c}}\right\}$where a and b are single digit natural numbers and c is some integer then $\left[\frac{\mathrm{b}+\mathrm{c}}{10\mathrm{a}}\right]$ is ____