Showing posts with label puzzles. Show all posts
Showing posts with label puzzles. Show all posts

Sorting pennies in the dark

I am recurrently amazed at the wonderful logic and math puzzles posted at Futility Closet.   Here's a recent one:
You’re in a pitch-dark room. On a table before you are 12 pennies. You know that 5 are heads up and 7 are tails up, but you don’t know which are which. By moving and flipping the coins you must produce two piles with an equal number of heads in each pile. How can you do this without seeing the coins?
I was not able to solve this on my own and had to peek at the answer.  Even after seeing the answer, it took me a long time to comprehend why it works.

I'll add some thoughts in the Comments section, but for the answer, go to Futility Closet.

Fiendishly tricky geometry puzzle

Start with a piece of paper 8" x 8", as shown on the left.  Make the two cuts shown.

Then shift the big lower-left piece up and to the left and move the triangle from the upper left corner to the lower right one.

The area that used to be 8x8 = 64 square inches now appears to be 9x7 = 63 square inches.  Where is the fallacy?

I pondered this for way too long, and finally had to cut some physical pieces of paper to solve the paradox.

The puzzle was originally created by or published by the famous Sam Loyd; I found it in the Futility Closet.

"En passant" chess puzzle

Futility Closet posts some very interesting chess puzzles, and the one above is one of best I have seen.

White plays B-g2+.  Black responds with pawn to d5, which (he says) blocks the check and uncovers a checkmate by the black bishop at c8.   White responds that the black pawn never got to/can't go to d5, because the white pawn takes it "en passant" at d6. 

More at the link (puzzle from Heinrich Fraenkel, Adventure in Chess, 1951.)

A simple math puzzle


A ball 13 inches in diameter has a 5-inch hole drilled through the center. How deep is the hole?

You can do this one in your head.  The answer is in the comment section.

Found at Futility Closet, where it was credited to Henry Dudeny.

Clues for building words in cryptic crosswords

Crypic crossword puzzles are way different (and more challenging) than conventional ones.  In addition to having a definition of the word, the cryptic clue also has some other method of ascertaining what the answer is.  It may be hidden in the clue, presented as an anagram, redefined in a second way, presented as a homonym or reversed word or initial letters of words, etc.

Sometimes it's necessary to "build" the word using clues that refer to the individual letters (or pairs of letters) in the word.  I started doing cryptics about 40 years ago, and began keeping a list of words that signalled individual letters.  Here is a certainly-incomplete-but-better-than-nothing compilation of clues I've encountered over the years.  Cryptic puzzlers are welcome to make use of it; others will find this curiously inexplicable and should just pass on to other items in the blog.

A = article, one, high grade, adult, answer, ace, number one, high mark, area, an, acre, argon, American

B = bee, British, bachelor, black, brown, second grade/second rate, born, Bible, boy, bishop, low budget, blue, book, bass, number 2

C = 100, around, cold, Canadian, Catholic, Conservative, catcher, century, about, $100, college, contralto, heroin, penny, average, carbon, Celsius, chapter, 4/4 time, copyright, major key, speed of light, note, city

D = 500, democrat, died, down, dead, heavy hydrogen/deuterium, penny/copper, Dutch, Germany, date, day, below average, daughter

E = east, direction, English, Easter, error, energy, excellent, failing, low mark/sign of failure, earl, empty, electronic

F = loud, full, French, female, fluid, Fahrenheit, fluorine, folio, Friday, fine, bass clef, federal, father, forte

G = German, gravity, grand, great, $1000, good, gee, gulf, for general audience, George, girl, Greek, treble clef, gender, general, game

H = hot, hit, hydrogen, gas, height, hospital, hard, husband, hour, heroin/horse, hotel, hundred, aspiration, goal posts

I = me, myself/self, first person, one, ego, island, ioidine, intelligence, Italy, interest, Interstate, electric current

J = Jack, judge, joule, fish hook

K = king, 1000/grand, kilo, king, potassium, killed, 3280.8 feet

L = long, left, latitude, line, Latin, liquid, fifty, lake, length, liberal, lira, lady, little, Lutheran, pound, fifty, lira

M = 1000, million, master, meter, mark, married, French man, mass, male/masculine, meridian/noon, million, Monday, grand, Bond character, medium, mile

N = north, direction, new, name, Norse, pole, northern, Navy, nitrogen, number, neutron, Newton, normal, noun

O = love, nothing, zero/zilch, ring, globe/ball, hoop/wheel, disc, old, egg, oxygen, oriental, doughnut/bagel, goose egg, no, cipher, ocean, gasket, overhead, orange, out, round

P = page, soft, quiet, penny/copper/pence, pale, piano, peso, power, pint, parking sign, petite, pressure, pawn, first person, passing, past, pepper

Q = queen, question

R = republican, red, right, river, king, ruble, royal/rex, retired, Roman, range, resistance, rare, rose, radius, restricted, radical, rod, not for children

S = south, direction, southern, short, pole, shilling, small, second, sulfur, Sabbath, satisfactory, skinhead, shilling, Saturday, Sunday, son, soprano, sibilant, turn, school, wavy line, salt

T = time, kind of square, tenor, testament, true, tritium, teaspoon, tense, car, ton, Tuesday, cross, shirt, tackle

U = university, hairpin turn, uranium, up, turn, bent, college, horseshoe, turnabout, uncle

V = five, flying geese, sign of victory, vice, verb, voltage, velocity, volume, victory, against, verse, vanadium, violet, fifth of vodka, style of neckline

W = west, direction, woman, with, white, wife, water, wide, watt, Wednesday, wulfram/tungsten

X = ten, cross, unknown, times/by, adult rating, kiss, wrong, chromosome, variable, spot/treasure site, illiterate signature, chi

Y = club, yard, slingshot, yttrium, year, men’s club, fork, fourth of July, yen, chromosome, twenty-fifth

Z = French movie/Montand movie, atomic number, last letter/character, zip, twenty-sixth, zone, zigzag