Alg/NT
Hypatia owns a large number of stones. When split into groups of 50, they observe that there are 30 left over. When split into groups of 70, they observe that there are 40 left over. What is the smallest number of stones they could have?
180
Euler is trying to construct a circle with the same area as a unit square. We know this is impossible, but if it was possible, what would the radius of this circle be?
1/sqrt(pi)
Plato rolls 2 regular 6-sided dice. What's the chance they roll a 3?
1/18
What does FLT stand for?
Fermat's Little Theorem
Turing writes integers from 1 to n, and observes that exactly one of the integers they wrote has precisely 7 factors. What is the largest n could be?
728 (3^6-1)
Euclid folds a piece of paper along a line parallel to one of its sides. The resulting folded paper has 3/4 the area of the original paper. How far is the crease from the side of the paper?
1/4
Cauchy wants to split 10 pencils amongst himself and 3 friends. How many ways are there for him to do this?
286 (13C3)
Who was the inventor of the computer?
Alan Turing
Noether has some number of red pencils and some number of blue pencils. Red pencils can last 7 days and blue pencils can last 9. She observes that, with her current collection of pencils, she can go another 100 days without getting new pencils. If it's given that Noether has at least 2 blue pencils, how many red pencils does she have?
4
Blessed by Fermat! Your next correct answer gets you x2 points!
:3
Fibonacci owns 5 2x1 dominos and a 2x5 board. How many ways are there for them to place all five dominos on the board such that no two dominos overlap and no domino goes off the board?
8
Who posed "23 problems for the new millenium?"
Hilbert
Hilbert owns a carpet that measures A > 0 meters across and B > 0 meters long. If the perimeter of this carpet is twice its area, find one possible (A, B).
4A+4B = AB must hold.
Gauss owns a set of tetrahedral dice. One of these dice has a side length of 1 centimeter. What's the volume of this die?
sqrt(2) / 12
How many subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} have no consecutive numbers?
89 (10th Fibonnacci Number)
Name a millenium problem.
Poincaré conjecture
Birch and Swinnerton-Dyer conjecture
Hodge conjecture
Navier–Stokes existence and smoothness
P versus NP
Riemann hypothesis
Yang–Mills existence and mass gap
Find the roots of:
3x^3-5x^2-11x-3 = 0
x=-1, x=3, x=-1/3
Triangle ABC has AB=5, BC=7, AC=8. A circle centered at O is inscribed in ABC. What is AO^2?
12
Diophantine picks 3 points on a unit circle at random. What is the probability that they form a triangle that contains the center of the circle in its area?
1/4
Name an UNSOLVED problem that also isnt a millenium problem.
:3