Let's determine $k$ so that the expression

$$
x^{2}+2 x+k
$$

is greater than 10 for all values of $x$.
The given expression can also be written as:

$$
(x+1)^{2}+(k-1)
$$

since $(x+1)^{2}$ is always a positive number, the given expression is greater than 10 for all values of $x$ if

$$
k-1>10
$$

or if

$$
k>11
$$

(Nándor Ehrenfeld, Nyitra.)

Number of solutions: 50.