Piecemeal

The following successful though illegal operation is reported by Professor A. Gloden in Sphinx, Volume VI, Number 7. In multiplying 6 2/3 by 4 4/5 a student first found the product of the integers, 6 × 4 = 24. He then reduced the fractions to the common denominator … and divided the product of the numerators 10 × 12 by the common denominator 15. The result 24 + 8 = 32 is correct.

In the same way he obtained the correct value of the product 9 3/5 × 2 2/4.

— “Curiosa,” Scripta Mathematica, October 1936

| Science & Math

Checkered Doughnuts

toroidal magic square - from mathematical circles

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.

toroidal chess problem, from petrovic, mathematics and chess

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

Hint: The solution comprises only two lines.

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| Puzzles · Science & Math

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.”

| Language · Science & Math

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.
| Science & Math

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

| Science & Math · Society

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?

| Language · Quotations · Science & Math

Thin Thinking

http://commons.wikimedia.org/wiki/File:San_Juan_Bautista_El_Greco.jpg

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?

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| Art · Puzzles · Science & Math