$\textbf{Butcher}$

A clerk at a butcher shop is five feet ten inches tall and wears size $13$ sneakers. What does he weigh?

$\textbf{Mountain}$

Before Mt. Everest was discovered, what was the highest mountain on earth?

$\textbf{Interesting Word}$

Which word in English is always spelled incorrectly?

$\textbf{Picture}$

$\textbf{Race}$

Joe has just passed the person in the second place of a marathon. What position is he in now?

$\textbf{Yolk}$

$\textbf{Haystacks}$

$\textbf{Son}$

$\textbf{The Pet Inc}$

The Pet Inc is owned by three gentlemen pets: a dog, a cat, and a pig. One day, while they are chatting to each other. Mr. Pig says: "Isn't it a bit odd that our surnames match our species, but none of our surnames matches our own species?" The dog replies: "Yes, but does it matter?" Can you relate their surnames and species?

$\textbf{Someone's Name}$

Someone's mother has four sons: North, West and South. What is the name of the fourth son. You are asked to write down the name of the fourth son. What will you write?

$\textbf{Number of Routes}$

The shortest route from point $A$ to $B$ takes $10$ steps. How many such routes are there that do not pass point $C$?

A driver travels for $2$ hours at $60$ miles per hour, during which her car gets $30$ miles per gallon of gasoline. She is paid $\$0.50$ per mile, and her only expense is gasoline at $\$2.00$ per gallon. What is her net rate of pay, in dollars per hour, after this expense?

How many $4$-digit positive integers (that is, integers between $1000$ and $9999$, inclusive) having only even digits are divisible by $5?$

The $25$ integers from $-10$ to $14,$ inclusive, can be arranged to form a $5$-by-$5$ square in which the sum of the numbers in each row, the sum of the numbers in each column, and the sum of the numbers along each of the main diagonals are all the same. What is the value of this common sum?

In the plane figure shown below, $3$ of the unit squares have been shaded. What is the least number of additional unit squares that must be shaded so that the resulting figure has two lines of symmetry?

Seven cubes, whose volumes are $1$, $8$, $27$, $64$, $125$, $216$, and $343$ cubic units, are stacked vertically to form a tower in which the volumes of the cubes decrease from bottom to top. Except for the bottom cube, the bottom face of each cube lies completely on top of the cube below it. What is the total surface area of the tower (including the bottom) in square units?

What is the median of the following list of $4040$ numbers?

$$1, 2, 3, ..., 2020, 1^2, 2^2, 3^2, ..., 2020^2$$

How many solutions does the equation $\tan{(2x)} = \cos{(\tfrac{x}{2})}$ have on the interval $[0, 2\pi]?$

There is a unique positive integer $n$ such that $$\log_2{(\log_{16}{n})} = \log_4{(\log_4{n})}$$ What is the sum of the digits of $n?$

A frog sitting at the point $(1, 2)$ begins a sequence of jumps, where each jump is parallel to one of the coordinate axes and has length $1$, and the direction of each jump (up, down, right, or left) is chosen independently at random. The sequence ends when the frog reaches a side of the square with vertices $(0,0), (0,4), (4,4),$ and $(4,0)$. What is the probability that the sequence of jumps ends on a vertical side of the square?

Line $\ell$ in the coordinate plane has the equation $3x - 5y + 40 = 0$. This line is rotated $45^{\circ}$ counterclockwise about the point $(20, 20)$ to obtain line $k$. What is the $x$-coordinate of the $x$-intercept of line $k$?

There are integers $a$, $b$, and $c$, each greater than 1, such that\[\sqrt[a]{N \sqrt[b]{N \sqrt[c]{N}}} = \sqrt[36]{N^{25}}\]for all $N > 1$. What is $b$?