To find me, you must first find my pairs, A swarm of creatures, skittering inside walls, Torturing the old way, sometimes using a chair, A powerful figure, there until its empire falls, Or some activities, one might enjoy in their lair. Who am I?

A man is only capable of telling the truth four hours a day, and they are either TTFTT or TFTTT (equiprobable). On the other twenty hours, he lies. All hours between 7pm and 6am are night, 7am and 11am are morning, noon and 4pm are afternoon, 5pm and 6pm are evening. He gives these statements in ...

My prefix has won the fights My infix marks the start of flights My suffix you can almost solve My whole makes friendly rubber revolve What am I?

The image below holds a secret. The question is: Which letter should be placed on the question mark and why? HINTS, more if needed

You are the lead mail inspector for a large prison. One of your jobs is to check all incoming and outgoing mail for any contraband and for any hidden information or codes, which are often of a criminal nature. One of the past repeat-offender prisoners, Daryl, has just attempted to mail a Valentin...

The Pawn March Problem is something I just came up with, and I thought it was interesting enough to share. White has a line of $n$ pawns on an infinite chess board, all on rank 0 (negative positions are legal, and pawns may never make double moves). Black has a single rook on $ωω$. Assuming opt...