The June 2023 Carnival of Mathematics # 216 at Eddie’s Math and Calculator Blog has the rather arresting item concerning Peirce’s Law from the American logician Charles Sanders Peirce (1839 – 1914).
“Peirce’s Law: Jon Awbrey of the Inquiry Into Inquiry blog
This article explains Pierce’s Law and provides the proof of the law. The proof is provided in two ways: by reason and graphically. Simply put, for propositions P and Q, the law states:
P must be true if there exists Q such that the statement “if P then Q” is true. In symbols:
(( P ⇒ Q) ⇒ P) ⇒ P
The law is an interesting tongue twister to say the least.”
Perhaps another way of saying it is “if the implication P ⇒ Q implies that P is true, then P must be true.” Still, it sounds weird.
See Peirce’s Law
(Update 6/20/2023) Appendix: Valid Argument Continue reading
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.
This is a straight-forward problem from Five Hundred Mathematical Challenges.
