2026 Pi Day
Competition
Join us for a lunar adventure! This year's theme is "The Moon is Made of Cheese". Solve problems, eat pie, and shoot for the stars!
Event Details
When
March 14, 2026
9:00 AM - 1:30 PM
Where
Maria Carrillo High School
Santa Rosa, CA
Who
5th - 8th Grade Students
Individual & Team Rounds
Warm Up!
Check out the problems from last year's competition (2025).
Prepare for Liftoff
Practice makes perfect. We've selected some of our favorite problems from the 2025 Pi Day Competition for you to try. Grab a pencil and see if you can solve them!
Individual Round Highlights
Try these selected problems from the 2025 Individual Round!
What is the remainder when the number $31415926535$ is divided by $3$?
Show Answer
2. Sum of digits: $3+1+4+1+5+9+2+6+5+3+5 = 44$. $44 \div 3 = 14$ remainder $2$.
In how many ways can Wallis scramble up the letters of the word "pizza" to form different words? ("zapiz" and "aipzz" are two examples) Note that the two z's are indistinguishable!
Show Answer
60. There are 5 letters with 2 z's. The formula is $\frac{5!}{2!} = \frac{120}{2} = 60$.
Wallis is practicing for a typing competition. His average typing speed is 80 wpm. There are two parts of the competition. One has 100 words and the other has 240 words. If there is a 10 minute break in between, how much time will it take for him to complete the competition?
Show Answer
14 minutes and 15 seconds. Total words = 340. Time typing = $340/80 = 4.25$ minutes ($4$ mins $15$ sec). Add $10$ min break = $14$ mins $15$ sec.
The first few terms of the Fibonacci sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... The ratio between consecutive terms approaches the golden ratio, which is close to the ratio between a mile and a kilometer. Wallis sees a road sign saying her destination is 90 miles away. Use the Fibonacci Sequence to estimate how many kilometers she is away. Express your answer as an integer.
Show Answer
144 (or 145/146). 89 is a Fibonacci number close to 90. The next term is 144. Since 1 mile $\approx$ 1.6 km, and $\Phi \approx 1.6$, the next Fib number approximates the conversion.
Wallis and Willis plan to meet at Pie Place. Both of them will arrive at any time between 9:00 am and 11:00 am, but they will only wait 40 minutes for each other. What is the probability that they will meet?
Show Answer
5/9. This is a geometric probability problem. The meeting area is the region $|x-y| \le 40$ within a $120 \times 120$ square. The area of non-meeting (two triangles corners) is $80 \times 80 = 6400$. Total area is $14400$. Area of meeting $14400 - 6400 = 8000$. Prob = $8000/14400 = 5/9$.
Team Round Highlights
Grab a friend and solve these together!
Room 1: Willis knows that an octave is defined as a certain pitch that has double the frequency of another note. In order to shatter Count Count's eardrums, Willis needs to sing at least three octaves higher than an A4 (which is 440 Hz). What is the minimum value (in Hz) that she can sing?
Show Solution
$440 \times 2^3 = 440 \times 8 = $ 3520 Hz.
Room 6: The Imaginary Man speaks of a "mine number" with these
properties:
\[ (\text{mine number})^2 = -1 \]
\[ (\text{mine number})^3 = -(\text{mine number}) \]
\[ (\text{mine number})^4 = 1 \]
(A) What is the value of $(\text{mine number})^5$?
(B) What is the value of $(\text{mine number})^{12}$?
Show Solution
(A) $(\text{mine number})^5 = (\text{mine number})^4 \cdot (\text{mine number}) =
1 \cdot (\text{mine number}) = $ mine number.
(B) $(\text{mine number})^{12} = ((\text{mine number})^4)^3 = 1^3 = $
1.
Room 5: A vending machine gives a fraction of a candy bar based on
payment:
Option 2: Pay $\frac{\pi}{6}$ dollars, get $\frac{1}{\sqrt{3}}$ bar.
Option 3: Pay $\frac{\pi}{4}$ dollars, get $1$ bar.
Option 4: Pay $\frac{\pi}{3}$ dollars, get $\sqrt{3}$ bars.
If Willis wants to get exactly 1 candy bar, how much money will she need to pay?
Show Solution
Option 3 gives exactly 1 bar. Pay $\frac{\pi}{4}$ dollars.