$a, b, c, d, e, f, g, h$ are distinct elements in the set $\{-7, -5, -3, -2, 2, 4, 6, 13\}$. The minimum value of $(a+b+c+d)^2+(e+f+g+h)^2$ is

In a battle,$70\%$ of the soldiers lost one eye,$80\%$ lost one ear,$75\%$ lost one arm,and $85\%$ lost one leg. If $x\%$ of the soldiers lost all four,what is the minimum value of $x$?

In a battle,$70\%$ of the combatants lost one eye,$80\%$ an ear,$75\%$ an arm,$85\%$ a leg,and $x\%$ lost all the four limbs. The minimum value of $x$ is:

The number of $4$-digit numbers which are neither a multiple of $7$ nor a multiple of $3$ is ..... .

In a school,there are $20$ teachers who teach mathematics or physics. Of these,$12$ teach mathematics and $4$ teach both physics and mathematics. How many teach physics?

Consider a three-digit number $N = 100x + 10y + z$,where $x, y, z$ are the digits at the hundreds,tens,and units places respectively. The number satisfies the following properties:
$I$. If its digits in the units place and tens place are interchanged,the number increases by $36$.
$II$. If its digits in the units place and hundreds place are interchanged,the number decreases by $198$.
If the digits in the tens place and hundreds place are interchanged,then the number: