Puzzle: The Chinese Farmer

A Chinese landowner wanted a farmer to work for 6 days for him. The reward: a slab of gold. The price: solving a riddle.
"I'll pay you per day: after day 1, you'll have one sixth of the gold, the next, two-sixths, et cetera, until after 6 days, you have the entire slab of gold. How do I do that, though?"
"Easy. Cut the slab into 6 equal parts, and give me one part each day."
"Ah", said the landowner. "But you can only cut the slab twice."
"Pff", said the farmer. "Still easy."

(Use rot13 to see the solution)
"Phg gur fyno gjvpr gb perngr guerr cvrprf: bar cvrpr (N) gung vf bar fvkgu bs gur fyno, bar (O) gung vf gjb-fvkguf (bar guveq) naq bar (P) gung vf guerr-fvkguf (unys).
Ba gur svefg qnl, tvir zr cvrpr N.
Ba gur frpbaq qnl, tvir zr cvrpr O naq V'yy tvir lbh onpx cvrpr N.
Ba gur guveq qnl, tvir zr cvrpr N onpx. V abj unir cvrprf N naq O, juvpu gbtrgure ner guerr-fvkguf.
Ba gur sbhegu qnl, tvir zr cvrpr P naq V'yy tvir lbh cvrpr O. V abj unir cvrprf N naq P, sbhe-fvkguf.
Ba gur svsgu qnl, tvir zr cvrpr O naq V'yy tvir lbh cvrpr N va erghea. V abj unir cvrprf O naq P, svir-fvkguf.
Naq svanyyl, ba gur fvkgu qnl, tvir zr cvrpr N naq V unir nyy guerr cvrprf, gur ragver fyno bs tbyq."

Needless to say, the landowner hires the farmer and retains him at a nice wage for the rest of his life.

Posted by cronopio at 01:38 PM

The AK47 problem

Cyberspace Rendezvous pointed me to a Wikipedia list of cognitive biases.
This puzzle challenges these biases.

You see four cards: 'A', 'K', '4' and '7'.
All cards have a number on one side and a letter on the other.
Check if the following proposition holds for each card, turning as few cards as possible:
"If there's a vowel on one side, then there's an even number on the other side."
How many cards to you turn, which ones, and why?

The answer, as always, is in rot-13.

Rirelbar (pbeerpgyl) purpxf 'N'.
Gur arkg pneq vf uneqre.
Fbzr crbcyr pubbfr 'X'. Jebat: gur cebcbfvgvba vf abg nobhg pneqf jvgu pbafbanagf.
Fbzr crbcyr pubbfr '4', zvfgnxrayl nffhzvat gung gur erirefr bs gur cebcbfvgvba fubhyq ubyq.
Gur pneq lbh arrq vf '7': vs vg unf n ibjry, gung snyfvsvrf gur cebcbfvgvba.
N terng rknzcyr bs pbasvezngvba ovnf.

Posted by cronopio at 03:06 PM

Sorting the Hats

No, this isn't about the Sorting Hat that wanted to put Harry Potter in the wrong house of Hogwarts, it's a puzzle.

Imagine that there are 60 dwarves that live in a cave. All dwarves wear hats. Some dwarves wear red hats, others wear blue hats. For some reason, no dwarf knows the color of his own hat, and in the cave, it's also too dark to see any other dwarf's hat color.
The dwarves now want to stand in a line outside their cave, so that the line consists of all the red-hatted dwarves first, and then all the blue-hatted ones. Or the other way round, that's irrelevant. The only important thing is that all the blue guys stand next to each other, and so do all the reds.
These dwarves must exit the cave one by one and immediately take their place in the line (the first dwarf can stands wherever he likes). They can't talk among each other, and they can't change their position once they've picked one.
How do the dwarves manage to line up in two groups, one red, one blue?

Here's the solution. I've rot13'd it, go to the rot13 site to decode.

Qjnes ahzore 1 whfg fgnaqf naljurer.
Qjnes ahzore 2 fgnaqf gb gur yrsg be evtug bs qjnes 1.
Nal sbyybjvat qjnes qbrf gur sbyybjvat:
-Vs nyy gur qjneirf' ungf ner gur fnzr pbybe, ur fgnaqf ba rvgure fvqr.
-Vs gurer ner gjb pbybef va gur yvar, gur qjnes fdhrrmrf va gur cbfvgvba jurer bar pbybe raqf naq gur arkg bar ortvaf.
Guvf jnl, gur qjnesf ner nyjnlf yvarq hc nf oyhr svefg, erq arkg, be ivpr irefn.

Posted by cronopio at 02:35 PM

The Eight Cue Balls

Here is another interesting puzzle.
The answer, rot13'd to prevent sneak peeking, is below.

I give you 8 cue balls, identical in appearance, and a scale.
Of these 8 cue balls, one is slightly heavier than the other 7, but not enough for you to notice when you hold it.
The scale can only tell you that it's balanced, or if it's not balanced, which side of the scale is heavier.
You can use the scale 2 (that's two) times. How do you find out which is the heavier cue ball?

Boivbhfyl, fgnegvat jvgu sbhe phr onyyf ba rnpu fvqr bs gur fpnyr jvyy trg lbh abjurer, orpnhfr lbh jvyy unir gb jrvtu guerr gvzrf.

Gur gevpx vf gung vs lbh jrvtu phr onyyf jvgu gur fpnyr, lbh nyfb tnva vasbezngvba nobhg gur onyyf lbh ner ABG jrvtuvat.

Urer'f ubj lbh qb vg.
Chg guerr phr onyyf ba rnpu fvqr bs gur fpnyr, yrnir gjb ba gur gnoyr.

Vs gurl ner onynaprq, jrvtu gur gjb erznvavat barf. Juvpurire vf fubja nf urnivre vf gur phr onyy lbh'er ybbxvat sbe.

To decode, use the rot13 converter.

Posted by cronopio at 01:00 PM

Not pr0n

Someone pointed me to this fascinating Web game, apparently "the hardest riddle on the internet". The goal of each puzzle in this game is to get to the next puzzle, and unlike most computer games, you can't win simply by applying the principle of banging your head against the door until it gives way. I'm now at level 8, and there's 134 levels (and growing).
Notpron is a refreshing change from games like Crimson Room, which mostly gauges your ability to point and click. If you play this last game, be warned: there's a URL in it that refers to a nonexistent page.

Posted by cronopio at 12:55 PM

I have dishonored my neurons and will now commit sudoku

In the UK, a new type of number puzzle is apparently all the rage: sudoku. This game, invented in North America 25 years ago, migrated to Japan where it got its current name. It then crossed the globe again to the United Kingdom and is becoming a regular feature in many newspapers there.

The rules of the game are simple: You are presented with a 9x9 grid of squares, divided into 9 boxes of 3x3. Some of the squares have numbers in them. Your task, young Jedi, is to fill in the remaining squares so that the whole grid obeys the following rules:

  • Each square contains a digit from 1 through 9
  • No row of the grid has the same digit twice
  • No column of the grid has the same digit twice
  • No 3x3 box has the same digit twice

If this sounds easy, think again. You can find sudokus at The Sudoku Site and get a fresh one every day at The Daily Sudoku. Enjoy your sudoku but go easy on the wasabi.

Posted by cronopio at 02:15 PM

Puzzles and Riddles 2: Solution

Here's the solution to the problem of the Three Boxes. I've rot-13'd it in case you didn't see the original riddle yet.

Lbh fubhyq fjvgpu; fjvgpuvat gb gur bgure obk qbhoyrf lbhe punaprf.

Guvf frrzf pbhagrevaghvgvir, ohg vs lbh erpbafgehpg nyy cbffvoyr fpranevbf, vg npghnyyl gheaf bhg gb or pbeerpg. Urer'f ubj vg jbexf.

Yrg'f ynory gur obkrf N, O naq P. Abj nffhzr gung lbh vavgvnyyl nyjnlf cvpx obk N. Vs gur cevmr vf va obk N, fjvgpuvat vf n onq vqrn. Vs, ubjrire, gur cevmr vf va obk O be P, gur bar erznvavat obk vf erzbirq naq fjvgpuvat jvyy trg lbh gur cevmr. Va bar guveq bs pnfrf, gur cevmr vf va N; va gjb guveqf, vg'f va O be P. Gurersber, fjvgpuvat qbhoyrf lbhe punaprf sebz bar guveq gb gjb guveqf; va bgure jbeqf, vg qbhoyrf lbhe punaprf.

Posted by cronopio at 01:50 AM

Puzzles and Riddles 2

An all-new logical puzzle for you:

The Three Boxes

In a quiz show, you are shown three identical, closed boxes. One of these boxes contains a prize. You are asked to pick a box. You do so (at random).

The quizmaster now removes one of the two boxes you didn't pick, and shows it to be empty.

He now asks you if you'd like to change your mind about your choice of box. Do you switch to the one remaining box, stick with your original choice, or doesnt it matter?

Mail me your solution. Next week, I'll reveal the answer.

Posted by cronopio at 09:21 PM

Puzzles and Riddles

From time to time, logical riddles grab me and keep me fascinated for some time. Over the years, I've come across some really great ones, so, for as long as the fascination holds, I'll try to give you some.

I prefer the type of logical puzzle that doesn't require a piece of paper and/or a higher knowledge of mathematics to solve. My first example is a good one.

Why are manhole covers round (rather than square)?

There's a very simple and logical answer to that question. Try and guess it before you read the rest of the entry. It might take some thought.

I was expecting you to read this too soon, so I rot13'd the answer for you to keep you guessing a little longer:

Znaubyr pbiref ner ebhaq fb gurl pna'g snyy vagb gur ubyr gung gurl pbire. N fdhner znaubyr pbire pbhyq snyy vagb gur ubyr naq frevbhfyl vawher gur crefba va gur frjre, fvapr gur qvntbany bs gur ubyr vf ybatre guna gur fvqrf bs gur pbire.

See? Once you see the solution, it makes a lot of sense.

Posted by cronopio at 01:06 AM