This is a nice variation on a racing problem by Geoffrey Mott-Smith from 1954.
“On one side of the playground some of the children were holding foot-races, under a supervisor who handicapped each child according to age and size. In one race, she placed the big boy at the starting line, the little boy a few paces in front of the line, and she gave the little girl twice as much headstart over the little boy as he had over the big boy. The big boy won the race nevertheless. He overtook the little boy in 6 seconds, and the little girl 4 seconds later.
Assuming that all three runners maintained a uniform speed, how long did it take the little boy to overtake the little girl?”
See the Handicap Racing for solution.
The June 2023 
The Futility Closet website had the following 
Here is another problem from the “Challenges” section of the Quantum magazine.
This is a classic example of a mixture problem from Dan Griller that recalls my agonies of beginning algebra.
This is a nice puzzle from the Maths Masters team, Burkard Polster (aka Mathologer) and Marty Ross as part of their “Summer Quizzes” offerings.
This is a nifty 
One of the physics blogs I enjoy reading is by the mathematical physicist Peter Woit, called 
This is a Catriona Agg problem presented by itself, since it turned out to be the most challenging one I ever tried. Usually I can solve her problems in a few minutes or maybe hours, or sometimes days if they are especially challenging. But this problem has taken me weeks and I had to rely on a non-geometric argument. The problem is full of fascinating and unexpected relationships, but I couldn’t find a way to use them to prove the answer.
Here is another challenging problem from the Polish Mathematical Olympiads. Its generality will cause more thought than for a simpler, specific problem.
