This is a fairly challenging problem from BL Math Games.
“Find the volume of the solid obtained by rotating the region enclosed by y = x and y = x2 about the line y = x.”
See Slanted Volume of Revolution for solutions.
Monthly Archives: March 2026
Trump is a Markov Process
I debated posting this, but it is so rare that a human behavior would be such a perfect example of a mathematical principle that I couldn’t resist. The idea came from a great summary of the state of affairs with Trump by Anne Applebaum in The Atlantic. Continue reading
A Simple Ratio
This is a straight-forward problem by Ritvik Nayak from the Puzzle Sphere.
“Evaluate the ratio. It’s actually simpler than you might think.”
Apparently it is a sample problem from the Southeast Asian Math Olympiad (SEAMO).
See A Simple Ratio for solutions.
Language Students Problem
This is a problem from the 2001 American Invitational Mathematics Exam (AIME).
“Each of the 2000 students at a high school studies either Spanish or French, and some study both. The number who study Spanish is between 80 percent and 85 percent of the school population, and the number who study French is between 30 percent and 40 percent. Let m be the smallest number of students who could study both languages, and let M be the largest number of students who could study both languages. Find M – m.”
See Language Students Problem for a solution.
Root of the Problem
This is a problem from Presh Talwalkar.
“Given that x satisfies the equation:
x4 + x3 + x2 + x + 1 = 0
What is the value of
(x33 + 2/x22)(x22 + 3/x33)”
See Root of the Problem for solutions.