Tag Archives: Sudoku

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.

PuzzleNation Book Review: The Puzzle Lady vs. the Sudoku Lady

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Welcome to the third installment of PuzzleNation Book Reviews!

All of the books discussed and/or reviewed in PNBR articles are either directly or indirectly related to the world of puzzling, and hopefully you’ll find something to tickle your literary fancy in this entry or the entries to come.

Let’s get started!

Our book review post this time around features Parnell Hall’s novel The Puzzle Lady vs. the Sudoku Lady.

Cora Felton is known far and wide as the Puzzle Lady, powerhouse puzzlemaker and occasional crimesolver, but her reign may be over. Minami, the Sudoku Lady, has come from Japan to challenge Cora for pride, PR, and puzzle-bragging rights. But when dead bodies start turning up and Minami is fingered as the culprit, it’s up to Cora to clear the competition’s good name.

Now, before I get into the review, it’s confession time. This is the second time around for me with this book. I read it a few years ago, and didn’t particularly enjoy it. But I was also sick as a dog at the time, so I wanted to be sure that my general foul mood at the time didn’t impair my ability to appreciate what I was reading at the time.

Turns out my illness had nothing to do with it.

The Puzzle Lady vs. the Sudoku Lady is part of Parnell Hall’s Puzzle Lady Mystery series — which he’s been publishing at the rate of a book a year since 2000 — and I sincerely hope it’s not indicative of the rest of the series. The reader plows through a needlessly convoluted story, confronted by a population of unpleasant characters and a protagonist who is unlikable in the extreme. She’s more grating than curmudgeonly.

Now, to be fair, that’s not to say that bright spots in the novel don’t exist. Hall has a natural adeptness with wordplay and his nigh-Vaudevillian exchanges of dialogue are engaging. Sadly, however, both are severely undermined by the unsympathetic cast of characters.

The sudoku and crossword puzzles included within are both an interesting gimmick and a pleasant treat; my own penchant for puzzling would not be ignored, and I solved each puzzle as it appeared. Unfortunately, those were calm spots in an otherwise stormy narrative.

I must conclude that The Puzzle Lady vs. the Sudoku Lady is at best an uneven reading experience. (Though I might try another Puzzle Lady Mystery someday, for curiosity’s sake.)

Well, I hope you enjoyed the latest installment of PuzzleNation Book Reviews, and I look forward to more book discussions in the future. In the meantime, keep calm, puzzle on, and I’ll catch you later.

This is impossible!

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There are puzzles out there for every skill level, from super-easy to staggeringly challenging. And every once in a while, you will come across a puzzle that feels expressly engineered to be as difficult as possible, if not borderline mind-meltingly impossible, even for an experienced solver.

If you’ve ever suspected a puzzlesmith of such diabolical shenaniganry, you’ll probably feel vindicated by Sean Adams’s post on McSweeney’s Internet Tendency, a bitingly funny introduction from a (hopefully) mythical puzzle book.

Enjoy!

For when you get bored playing the expert level of Sudoku.

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Do you find your average Super-Challenging God-Level Expert Platinum Blond mode of Sudoku too easy?  Now you can prove it!

A pair of computer scientists from the  Babes-Bolyai University (Romania) and the University of Notre Dame (USA) have made some remarkable connections between Sudoku, the classic k-SAT problem, and the even more classic non-linear continuous dynamics.

Using these connections they’ve been able to come up with a “Richter Scale” to objectively determine the difficulty of a Sudoku puzzle.

So when you encounter a puzzle labelled hard and you find it easy all you need to do is to compute its η, a co-efficient that measures the hardness of the problem.

Simple as that! Now you can have both the challenge (or lack-thereof) of the Sudoku game plus figuring out just how badly the editors mischaracterized its difficulty level!

I’m off to try and figure out how well our Classic Sudoku difficulty ratings stack up….

Source: The Chaos Within Sudoku – A Richter Scale