This is another simple problem from the 2025 Math Calendar.
“The sum of x consecutive numbers is 529. Their average is x. What is x?”
For a bonus problem, not included in the calendar, what is the sequence of numbers?
See Number Average for a solution.
A while ago James Tanton provided a series of puzzles:
Puzzle #1 At what value between 0 and 1 does a horizontal line at that height produce two regions of equal area as shown on the graph of y = x2?
Puzzle #2 A horizontal line is drawn between the lines y = 0 and y = 1, dividing the graph of y = x2 into two regions as shown. At what height should that line be drawn so that the sum of the areas of these two regions is minimal?
Puzzle #3 A horizontal line is drawn between the lines y = 0 and y = 1, dividing the graph of y = xn into two regions as shown (n > 0). At what height should that line be drawn so that the sum of the areas of these two regions is minimal? Does that height depend on the value of n?
Puzzle #4 What horizontal line drawn between y = 0 and y = 1 on the graph of y = 2√x – 1 minimizes the sum of the two shaded areas shown?
See Double Areas Puzzles for solutions.
This is a puzzle from Futility Closet.
“A puzzle by Steven T., a systems engineer at the National Security Agency, from the NSA’s September 2016 Puzzle Periodical:
Three athletes (and only three athletes) participate in a series of track and field events. Points are awarded for 1st, 2nd, and 3rd place in each event (the same points for each event, i.e. 1st always gets “x” points, 2nd always gets “y” points, 3rd always gets “z” points), with x > y > z > 0, and all point values being integers.
The athletes are named Adam, Bob, and Charlie.
Question: Who finished second in the 100-meter dash (and why)?”
I thought this puzzle impossible at first. There didn’t seem to be enough information to solve it. But a bit of trial-and-error opened a path.
See NSA Track and Field Puzzle for solutions.
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.
Presh Talwalkar has an interesting new problem.
“Students and teachers found a recent test in New Zealand to be confusing and challenging for covering topics that were not taught in class.
For the equation below, find the value of k for which the equation has numerically equal but opposite signs (for example, 2 and –2):
”
The problem didn’t mention how old the students were, but the solution to another problem on the test indicates they needed to know calculus.
See Mystery Quadratic for a solution.
This is a nice problem from Five Hundred Mathematical Challenges.
“Problem 62. A plane flies from A to B and back again with a constant engine speed. Turn-around time may be neglected. Will the travel time be more with a wind of constant speed blowing in the direction from A to B than in still air? (Does you intuition agree?)”
See Air Travel for a solution.
This is a 2017 Center of Mathematics Problem of the Week.
“The average age of a 10 member committee is the same as it was 4 years ago, because an older aged member has been replaced by a younger aged member. How much younger is the young member than the older member they replaced?”
See the Young and Old Problem.
… I know I feel differently in the morning, after seeing the pictures and reading the stories of lives arbitrarily snuffed out and people who had little reduced to people who have nothing at all. But tonight I’m going to bed in a vicious mood, with a stomach so full of contempt for this poisoned republic and its brain-dead citizens that I can taste it in my mouth, like bile.
And the only thing I can think to ask God—if she does exists—is why, just for once, can’t you smite the wicked instead of the innocent?
Posted by billmon at 01:09 AM
(Billmon’s full post can now be found on the Internet Wayback Machine at https://web.archive.org/web/20051001001007/http://billmon.org/)
This 24 September 2005 post was made during the height (or depths) of the Iraq War during the Bush-Cheney regime. Also recall the other Bush debacle, Hurricane Katrina, was just the month before, August 23–31, 2005. We thought we were in the depths of depravity and had no inkling that we were only at the higher rings of hell.
This is an interesting algebra problem from BL’s Weekly Math Games, which is behind a subscription wall.
(a3 – b3)/(a – b)3 = 73/3,
what is a – b?”
In fact, it is possible to solve for a and b individually as well.
See a Tricky Ratio Puzzle for the solution.
(Updates 11/6/2024, 11/9/2024) Other Solutions Continue reading
