This is a problem from Barry Leung’s Math Games.
“Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. The winner is the first person to knock the bottle off the ledge. At each turn the probability that a player knocks the bottle off the ledge is ½, independently of what has happened before. What is the probability that Larry wins the game?”
See Knock the Bottle Problem for a solution.
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.
This is a Valentine’s Day puzzle from BL’s (Barry Leung) Math Games.
“Happy Valentine’s Day everyone, I hope you are having a euphoric moment, but if not, you can try this algebra puzzle about maximizing the expression LUV + LU + UV + LV given L + U + V = 12, where L, U, V are non-negative integers.”
See Maximizing Love for a solution.
This is another problem from BL’s Math Games.
“What fraction of the rectangle is colored? Assume that M and N are midpoints of the sides of the rectangle.”
That they are midpoints was not stated explicitly in the problem as given in front of the subscription wall, but from the comments it became evident this was the case.
Initially I actually assumed the line was positioned arbitrarily. What would be the solution in that case?
Answer to BL problem.
See ZigZag in Rectangle for a solution.
This problem is from BL’s Math Games.
“What’s the area of the red triangle?”
BL decided to see what kind of solution ChatGPT would come up with. After several tries and prompts it seemed to oblige. I don’t know what BL’s prompts were, and in the statement of the problem outside the subscription wall he never explicitly says what the problem is, namely, to find the area of the red triangle.
There also seems to be some ambiguity about the constraints on the problem, that is, how much of the appearance of the diagram should the solver assume?
See ChatGPT Problem for a solution.
This is an old puzzle from Catriona Agg that I found on BL’s Math Games website.
“All four triangles are equilateral. What fraction of the largest triangle is shaded?”
This problem turned out to be both easy and unexpectedly challenging, at least for me.
See Four Equilateral Triangles for solutions.
This is a slightly challenging problem from BL’s Math Games.
“In a square garden ABCD of side 10m, a sheep sets off from B and moves along BC at 30cm per minute. At the same time, you set off from C and move along edge CD at 40cm per minute. The question is, what’s the shortest distance between you and the sheep in meters?
This is somewhat an optimization problem because as you and the sheep move along the sides of the square at different rates, the distance in between varies as you can imagine.”
There’s at least one non-calculus solution and of course one calculus solution.
See Sheep in Garden Problem for solutions.
Here is a probability problem from BL’s Weekly Math Games. Normally I am not a fan of such problems, but this one seemed fairly straight-forward for a change.
“I hit the target 75% of the time. You hit the target 25% of the time. We aim at the same time, and only one bullet hits. What’s the probability it came from me?
Now as for this puzzle, it would be tempting to think that I am 3 times as good at hitting the target, but I am not!”
See Whose Bullet for a solution
Here is another problem from BL’s Weekly Math Games.
“For every point P on y = 2x2, areas A and B are equal. Find the equation for curve C.”
See Mystery Curve Puzzle for a solution
This is another puzzle from BL’s Weekly Math Games.
“a + b + c = 2, and
a2 + b2 + c2 = 12
where a, b, and c are real numbers. What is the difference between the maximum and minimum possible values of c?”
The original problem statement mentioned a fourth real number d, but I considered it a typo, since it was not involved in the problem.
See Sphere and Plane Puzzle for a solution.
