# Checkered Doughnuts

Roll this magic square into a tube by joining the upper and lower edges, then join the ends of the tube. Every row, column, and diagonal on the resulting torus will add to 34.

Bend this chessboard similarly into a torus, then mate in 4.

Hint: The solution comprises only two lines.

# Circular Argument

Thomas Edison offered this burlesque on perpetual motion. “There will always be a nine opposed to a six,” explains Sam Loyd, “and as nine weighs more than six, it will make the wheel revolve rapidly, as well as your head when you understand it thoroughly.”

# Quite Contrary

A contronym is a word with two contrary meanings, such as cleave or sanction (more here).

The word contronym itself has no double meaning. Is it a contronym?

“Not until I came along!” writes Charles Melton in Word Ways. “I declare that it is a contronym for the simple reason that it isn’t! It is both a self-opposite and not a self-opposite. QED.”

# A Violent Argument

A logic exercise by Lewis Carroll. What conclusion is implied by these premises?

1. Animals that do not kick are always unexcitable.
2. Donkeys have no horns.
3. A buffalo can always toss one over a gate.
4. No animals that kick are easy to swallow.
5. No hornless animal can toss one over a gate.
6. All animals are excitable except buffaloes.

# Bang!

If Brown hopes to throw a six in a game of dice and succeeds, we wouldn’t say he threw the six intentionally. If Brown puts his last cartridge into a six-chambered revolver, spins the chamber as he aims it at Smith, his archenemy, pulls the trigger, and kills Smith, we’d say he killed him intentionally. Does that make sense? In both cases Brown hoped for a certain result, in both cases the probability of that result was the same. If Brown didn’t intentionally throw a six, why did he intentionally shoot Smith?

— Leo Katz, Bad Acts and Guilty Minds, 1987

# Misc

• What time is it on the sun?
• PATERNAL, PARENTAL, and PRENATAL are anagrams.
• If forecastle is pronounced “fo’c’sle,” should forecast be pronounced “folks”?
• A clock’s second hand is its third hand.
• “The religion of one seems madness unto another.” — Thomas Browne

Bonus poser: In what sport does only the winning team travel backward?

# The Hooded Man

You say you know your brother.

Yet when your brother is hooded you are unable to identify him.

Therefore you both do and do not know your brother.

— Eubulides

# Thin Thinking

Some of the figures (particularly the holy ones) in El Greco paintings seem unnaturally tall and thin. An ophthalmologist surmised that the painter had a defect of vision that caused him to see people this way.

The zoologist Sir Peter Medawar pointed out that we can reject this conjecture on purely logical grounds. What was his insight?

# “The Unprovable Liar”

‘What I am saying cannot be proved.’

Suppose this statement can be proved. Then what it says must be true. But it says it cannot be proved. If we assume it can be proved, we prove it cannot be proved. So our supposition that it was provable is wrong. With that road closed to us, let’s try the only other one available — let’s suppose it cannot be proved. Since that is precisely what it says, then it is true after all. And this ends our proof of the above statement!

— Gary Hayden and Michael Picard, This Book Does Not Exist, 2009