Fermi Questions
2025
Geometry
Counting & Probability
Number Theory
100
The number of grilled cheeses consumed by Hopkins students and faculty on the annual Jack Lubin Grilled Cheese DayTM.
What is 103?
100
Prime factorization of 2025.
What is
3^4 * 5^2?
100
The driveway in front of Kyle's house is 20 feet wide and 100 feet long. If asphalt is ordered in a whole number of cubic yards, this is the number of cubic yards of asphalt that must be ordered to pave Kyle's driveway with a layer of asphalt three inches thick.
What is 19 cubic yards?
100
In the land of Noom, all nouns are 4-letter words with consonants at the beginning and end and a repeated vowel (a, e, i, o, or u) in the middle. This is the number of words in the vocabulary of the Noomites.
What is 2205?
100
This is the greatest prime factor of 204-154.
What is 7?
200
The number of times the phrase "skibidi toilet" was said by people in America in 2024.
What is 107?
200
The number of factors of 2025
What is 15?
200
The number of units in the length of the longest side of quadrilateral ABCD with vertices at A(0, 0), B(6, 0), C(8, 4) and D(5, 8) in simplest radical form.
What is
\sqrt{89}?
200
The number of 4-digit integers that have their digits in strictly ascending order.
What is 126?
200
The sum of the reciprocals of all of the integer factors of 18.
What is 0?
300
The number of slices of pizza consumed in the US every year.
What is 1010?
300
The difference between the perfect squares immediately after and immediately before 2025.
What is 180?
300
The ratio of the area of region I to the area of region III, given that all regions are squares, and region I has perimeter 12 units and region II has perimeter 24 units.
What is 1/9?
300
A pair of two distinct points is selected at random from the set P. This is the probability that the length of the segment formed by joining the chosen points is an integer.
P = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1),(3, 2), (3, 3)}
What is 1/2?
300
The value of a + b, given that a and b are positive integers such that ab = 48 and a − b = 8.
What is 16?
400
The number of Mathcounts chapter competition participants across the whole country per year.
What is 104?
400
Let x be the square root of 2025. This is the smallest number with exactly x factors.
What is 3600?
400
Ms. Williams is building a pig pen and has 48 feet of fence. This is the area of the largest pig pen she can build.
What is 144 square feet?
400
In a classroom there are 6 rows of 5 desks each. The seats are numbered 1-30 and each student is randomly assigned a seat at the beginning of the year. This is the probability, as a percent, that Jeff gets to sit in an end seat (seat at the end of a row and/or column).
What is 60%?
400
The units digit of ((134-87)2025)23.
What is 3?
500
The number of eggs all the chickens in the US lay in ten years.
What is 1012?
500
Let a1 = 165 and a2 = 150 and each subsequent term in the sequence be given by:
an = an-1 + an-2
This value of n has an = 2025.
What is 6?
500
Because of the awful 1 way streets in New Haven, Amy drives 13 meters East, then 12 meters North, then 7 meters West, and finally 4 meters South to get to her destination. This is the number of meters in the straight line path from her starting point to her destination.
What is 10?
500
Ms. Williams draws three cards at random, without replacement, from a deck of ten cards numbered 1 through 10. This is the probability that no two of the cards drawn have numbers that differ by exactly 1.
What is 7/15?
500
Suppose a and b are different prime numbers greater than 2. This is the number of whole-number divisors for the integer a(2a + b) − 2a2 + ab.
What is 8?