Tag Archives: Puzzle to solve

Sudoku: Every number in its place.

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Sudoku puzzles are as ubiquitous as reality shows these days, and enthusiastic solvers can find puzzles of nearly any difficulty with ease.

Sudoku puzzles are usually ranked from one to five stars, with five star puzzles being the most difficult. Difficulty can depend not only on the number of starting digits, but their placement and the level of deduction involved.

Sudoku enthusiasts were the first to notice that the lowest number of clues required for a unique solution is 17. Puzzles with 16 clues invariably had alternate solutions.

For comparison purposes, the average newspaper sudoku has 25 set numbers. The sudoku puzzles on PuzzleNation vary in difficulty, but our easy puzzles range from 30 to 36 clues and our expert puzzles range from 25 to 30 clues, with medium and hard puzzles clue counts falling in between.

But the 17-clue threshold was all conjecture until a mathematician from University College Dublin named Gary McGuire put in the time (and the computer processing power) to write a mathematical proof confirming the suspicions of sudoku enthusiasts.

He designed a specific computer algorithm to process various sudoku grid patterns, allowing him to cut down on the computing time necessary to verify his conjecture. (Even with the reduced computing time, it took 7 million CPU hours in total, a monumental amount of processing time.)

From the nature.com article:

The idea behind this was to search for what he calls unavoidable sets, or arrangements of numbers within the completed puzzle that are interchangeable and so could result in multiple solutions. To prevent the unavoidable sets from causing multiple solutions, the clues must overlap, or ‘hit’, the unavoidable sets. Once the unavoidable sets are found, it is a much smaller—although still non-trivial—computing task to show that no 16-clue puzzle can hit them all.

Of course, as I said before, difficulty isn’t just about the number of clues. The puzzle widely regarded as the world’s hardest sudoku puzzle has 21 clues, but their placement makes for a much more mentally-taxing solving exercise.

I guess it just goes to show the old real estate cliche is true: it’s all about location, location, location.

Puzzles in Pop Culture: Futurama

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Not so long ago, I wrote a post about cryptography in the real world, highlighting moments where codebreaking made a difference in crime solving and espionage, and sometimes changed the course of history.

And while the encryptions featured in today’s entry aren’t quite as world-changing, they just as interesting.

I’m talking about the alien languages that were featured in the background of the animated television show Futurama.

At least two ciphers have been employed by the writers and animators of the show — a third is rumored to have appeared in the fourth season of the show, but there hasn’t been confirmation of that — and they’ve proven to be an engaging Easter egg for puzzle fans.

The first is called Alien Language One, or Alienese, and it appeared in the background of the show from the pilot episode onward. It’s a simple one-to-one code, with symbols for all 26 letters and 10 digits in standard English. (Supposedly it was solved by some enterprising puzzlers within a half-hour of the show’s premiere.)

A second, far more complex encryption started appearing during the show’s second season, and it’s called Alien Language Two, or Alienese II, and it’s based on an autokey cipher.

Autokey ciphers are more involved than a standard encryption, because there’s no one-to-one organizational structure. Instead, the symbol for a given letter or number can change based on the symbol that precedes it.

I’ll let the folks at the Futurama Wiki explain:

Each symbol has a numerical value. To decode a message, the first symbol’s value is translated directly into a character (0=’A’, 1=’B’, and so on). For the remaining letters, you subtract the previous symbol’s numerical value. If the result is less than zero, you add 26. Then that number is converted into a character as before.

This is some high-level puzzling, considering it’s a background joke-delivery system on an animated show. (But, considering the show does jokes about Schrodinger and throwaway gags based on mathematical principles like taxicab numbers, I’m not at all surprised.)

Of course, those puzzle-lovers at The Simpsons couldn’t help but get in on the fun, using Alienese as a background gag in a reference to the show Lost.

The masterminds at Futurama are definitely puzzlers at heart, and more than worthy of recognition in the Puzzles in Pop Culture library.

Dangerous and disturbing this puzzle is.

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I couldn’t resist, it’s the only line in all six Star Wars movies that uses the word “puzzle,” and it’s a Yoda quote to boot!

Greetings, my fellow puzzlers! It’s Star Wars Day, and we here at PuzzleNation simply had to join in the festivities, so we’ve got two Star Wars themed puzzles for your enjoyment!

The first is a standard cryptogram of one of the series’ most famous quotations. This should be an easy one for crypto-fans and Star Wars devotees alike!

UOKOXJH LOKCSZ, POJXW JUC PCB WOXEOT IP VJFGOX ZK FGO MHCKO QJXW. KCQ GO SOUW PCB FC GOHD GZI ZK GZW WFXBUUHO JUJZKWF FGO OIDZXO. Z XOUXOF FGJF Z JI BKJSHO FC MCKEOP IP VJFGOX’W XORBOWF FC PCB ZK DOXWCK, SBF IP WGZD GJW VJHHOK BKTOX JFFJML, JKT Z’I JVXJZT IP IZWWZCK FC SXZKU PCB FC JHTOXJJK GJW VJZHOT. Z GJEO DHJMOT ZKVCXIJFZCK EZFJH FC FGO WBXEZEJH CV FGO XOSOHHZCK ZKFC FGO IOICXP WPWFOIW CV FGZW X2 BKZF. IP VJFGOX QZHH LKCQ GCQ FC XOFXZOEO ZF. PCB IBWF WOO FGZW TXCZT WJVOHP TOHZEOXOT FC GZI CK JHTOXJJK. FGZW ZW CBX ICWF TOWDOXJFO GCBX. GOHD IO, CSZ-QJK LOKCSZ. PCB’XO IP CKHP GCDO.

And the second is a Word Seek featuring characters from all six films (plus Ahsoka from the Clone Wars TV show). The entries in all caps are hidden within the grid, and once you’ve found them all, you’ll reveal a concealed message spelled out by the remaining letters!

AAYLA Secura
Admiral ACKBAR
AHSOKA Tano
ANAKIN
BAIL ORGANA
BEN KENOBI
Aunt BERU
BIGGS
BOBA FETT
BREN Derlin
CHEWBACCA
DARTH Vader
DENGAR
Jan DODONNA
Count DOOKU
EMPEROR
GREEDO
General GRIEVOUS
HAN SOLO
JABBA the Hutt
JANGO Fett
KIT FISTO
LANDO
LEIA
LUKE
LUMINARA Unduli
Darth MAUL
MAX REBO
MON MOTHMA
MOTTI
NEEDA
OBI-WAN
Uncle OWEN
OZZEL
PADME
PALPATINE
PIETT
QUI-GON
RANCOR
RIEEKAN
SHAAK TI
SIDIOUS
SKYWALKER
TARKIN
VEERS
WEDGE Antilles
WICKET
Mace WINDU
YODA

Good luck, and May the Fourth Be With You, puzzle Jedi!

Love and Other Puzzles

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You read stories about puzzle-centric cleverness all the time, whether it’s a real-life treasure hunt or saving Christmas through cryptography. But tales of puzzleriffic romance? Those are far more rare.

So when I was reminded of a particular bit of romantic wordplay fun, I couldn’t wait to share it with my fellow puzzlefiends.

C and G are one of those brilliantly matched couples that makes you smile just thinking of them. Marvelously compatible interests and senses of humor and general weirdness that makes relationships worthwhile.

G had several gifts picked out for C, but he wanted to surprise her with a little something extra, a bit of diabolical sweetness only a true puzzle devotee would love.

So, before C received each small token of affection, she was given a cryptic crossword (also known as a British-style crossword) clue to solve. Cryptic crossword clues involve both cunning wordplay and a definition. The number after the clue provides the number of letters in the answer word.

Here are the clues G created. Hopefully you can figure out the answers just as C did!

Really glitchy web address loaded between Tuesday and first of year (5)

Found, amidst mishap, pyramid’s content (5)

Begin tortured existence (5)

Thine enemy, in the end, belonging to us both (5)

Plus, there’s an added bonus: the four five-letter answers, when placed in order, form a phrase.

As it turns out, not only is romance NOT dead, but it’s far more clever than you may have expected.

 

 

 

[Many thanks to C and G for allowing me to share this lovely story with my fellow puzzlers.]

I’m gonna need a stepladder.

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Plenty of places claim they offer large crosswords for the truly devoted solver, but nobody holds a candle to the Ukraine, whose citizens crafted this 100-foot-tall monument to puzzling.

Located in the city of Lviv (Lvov, to Russian speakers), the puzzle is an art installation perfectly designed to keep visitors thoroughly challenged. The clues are scattered on landmarks throughout the city, further encouraging both tourism and brain-boosting.

The puzzle appears incomplete during the day, but at night, special lighting reveals the answers in fluorescent paint.

I can only hope this will inspire other communities to raise the stakes even higher. Crop crosswords that can only be solved with Google Maps! Landscaping sudoku hedges complete with topiary set numbers! Cowboy-style word searches where you actually lasso words on cattle!

Okay, maybe not that last one. But hey! At least I’m trying! The artists of Lviv have set the bar — not to mention the grid — pretty darn high.

Why do so many puzzles involve crossing rivers?

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Seriously, there’s the one with the cabbage, goat and wolf (and variations thereof), there’s the Bridges of Konigsberg, and this one. When it comes to weirdly common puzzle scenarios, it’s right up there with drawing paired socks at random and turning two triangles into four. Puzzlers might have too much free time on their hands. *laughs*

ANYWAY. I digress.

A buddy of mine sent me a brain teaser the other day, and it seemed like the perfect challenge for my fellow puzzle fans. Although it tends a bit more toward the mathematical-word-problem side than a straight brain teaser, I think it will get your deductive juices flowing!

Bridge and Torch

Four people come to a narrow bridge at night. Among them, they have one torch, which has to be carried in order for anyone to cross.

Only two people can cross the bridge at a time. Person A can cross the bridge in 1 minute, B in 2 minutes, C in 5 minutes, and D in 8 minutes. When two people cross the bridge together, they go at the slower person’s pace.

How can they all cross the bridge in 15 minutes or less?

(Oh, before I go… a quick bit of internet sleuthing reveals that this puzzle originated in Garth Sundem’s Brain Candy: Science, Paradoxes, Puzzles, Logic, and Illogic to Nourish Your Neurons. Credit where credit is due, always. Enjoy!)