Find the number of pairs $\left(m, n\right)$ of integers which satisfy the equation $m^3+6{ m}^2+5 m=27n^3+9n^2+9n+1.$

For what values of $b$ do the equations:

$1988x^2+bx+8891=0$ and $8891x^2+bx+1988=0$ have a common root?

Given that the equation in $x$ has at least a real root, find the range of $m.$

$\left(m^2-1\right)x^2-2(m+2)x+1=0$

Mr. Fat is going to pick three non-zero real number and Mr. Taf is going to arrange the three numbers as the coefficients of a quadratic equation.

$\square x^2+\square x+\square =0$

Mr. Fat wins the game if and only if the resulting equation has two distinct rational solutions. Who has a winning strategy?