# Oxford Entrance Exam Problem 6

The functions $$S$$ and $$T$$ are defined for real numbers by

$$S(x)=x+1$$ and $$T(x)=-x$$.

The function $$S$$ is applied $$s$$ times and the function $$T$$ is applied $$t$$ times, in some order, to produce the function

$$F(x)=8-x$$.

It is possible to deduce that

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