# My Interview with AoPS

AoPS recently interviewed me about my thoughts on math education and math contests. I shared a number of unconventional ideas around math education, including:

• Math isn’t always fun. Learning often feels awkward and uncomfortable. If our mantra is “Learning is Fun!” what message do we send, when it clearly isn’t?
• Using math creatively means students need to know why their algorithms work. Otherwise, it’s like telling a student how use red paint or blue paint, but never showing them how they combine to make purple.
• Studying a math curriculum without participating in a contest is like going to soccer practice every day without ever playing a game.
• Math contest rules are not the boss of you.
• Normalize frustration. Did I mention that learning isn’t fun?

# 2021 AIME I #9

Let $ABCD$ be an isosceles trapezoid with $AD = BC$ and $AB. Suppose that the distances from $A$ to lines $BC, CD$, and $BD$ are $15, 18,$ and $10$, respectively. Let $K$ be the area of $ABCD$. Find $\sqrt{2} \cdot K$.

# 2021 AIME I #8

(Note: I have the wrong problem number written in the video whiteboard.)

Find the number of integers $c$ such that the equation $||20|x|-x^2|-c|=21$ has $12$ distinct solutions.

# 2021 AIME I #7

Find the number of pairs $(m,n)$ of positive integers with $1 \le m < n \le 30$ such that there exists a real number $x$ satisfying $\sin(mx)+\sin(nx)=2$.

# 2021 AIME #5

Call a three-term strictly increasing arithmetic sequence of integers special if the sum of the squares of the three terms equals the product of the middle term and the square of the common difference. Find the sum of the third terms of all special sequences.

# 2021 AIME I #4

Find the number of ways $66$ identical coins can be separated into three nonempty piles so that there are fewer coins in the first pile than in the second pile and fewer coins in the second pile than the third pile.

# 2016 AIME I #15

Circles $\omega_1$ and $\omega_2$ intersect at points $X$ and $Y$. Line $l$ is tangent to $\omega_1$ and $\omega_2$ at $A$ and $B$, respectively, with line $AB$ closer to point $X$ than to $Y$. Circle $\omega$ passes through $A$ and $B$ intersecting $\omega_1$ again at $D \neq A$ and intersecting $\omega_2$ again at $C \neq B$. The three points $C, Y,$ and $D$ are collinear, $XC = 67, XY = 47,$ and $XD = 37$. Find $AB^2$.

# 2016 AIME I #14

Centered at each lattice point in the coordinate plane are a circle with radius 1/10 and a square with sides of length 1/5 whose sides are parallel to the coordinate axes. The line segment from (0,0) and (1001, 429) intersects m of the squares and n of the circles. Find m+n.

# 2016 AIME I #13

This one is the classic jumping frog with state diagrams, this time in the coordinate plane between a fence and river.

# 2016 AIME I #12

Find the least positive integer $m$ such that $m^2-m+11$ is a product of at least four not necessarily distinct primes.