FoxTrot's Sudoku-ometry [update 2]
Break out your books on calculus, sequences, binary and hexadecimal number systems, logarithms, algebra, geometry and trigonometry and get cracking -- or, if you're lazy, continue reading for the solution guide.
Note: Although we're infallible, please let us know of any errors in our calculations and we'll fix it.
[Update 2: hey, did you know it's actually called sudoku and not sodoku? Yeah, I forgot to tell my headline writer -- me. Fixed.]
Reader Comments (Page 1 of 1)
Arthur Sloane @ Oct 15th 2006 2:02PM
3+4 isn't 5 ...
Probot @ Oct 15th 2006 2:05PM
"3+4 isn't 5"
I think it's pretty impressive that they actually got the simplest equation wrong.
eM @ Oct 15th 2006 2:08PM
Well, FF-F8 isn't 3, either.
Chris Maguire @ Oct 15th 2006 2:09PM
If it's hexidecimal subtraction, FF-F8 should be 7, not 3 -- plus, there's already a 3 in that row. ;]
Sneak @ Oct 15th 2006 2:10PM
Thanks for this, I'll be happy to pass this along to my cousin who's in applied mathematics, I think he could see the real maigc in this game.
LordMinogue @ Oct 15th 2006 2:11PM
FF - F8 = 7!
15*15+15 - 15*15+8 = 15 - 8 = 7
Sad, you got the hexadecimal question wrong! For shame.
What compelled you to think the answer was 3!
Ross Miller @ Oct 15th 2006 2:12PM
Word to the wise: never blog OR do mathematics when full of medication (stupid pharyngitis ...)
All that should be fixed now; I'm betting by 5pm I'll have half the puzzle redone :p
LordMinogue @ Oct 15th 2006 2:23PM
Solved It!
173892645
986453217
452617938
841275369
765934821
329186754
597361482
614728593
238549176
VerticalEvent @ Oct 15th 2006 2:26PM
"15*15+15 - 15*15+8 = 15 - 8 = 7"
EEH! Wrong.
It's (15*16^1 + 15*16^0) - (15*16 + 8*15^0)
= 7
Right answer, wrong method (it's BASED 16, not 15)
Scutpuppy @ Oct 15th 2006 2:33PM
Oh. My. Goodness. That's an amazing idea.
HallwayGiant @ Oct 15th 2006 2:35PM
Solved...but definitely not first. >_>
Completed image:
http://img.photobucket.com/albums/v185/Cardinal_Fang/ftsudoku-solve.jpg
eialba @ Oct 15th 2006 2:46PM
The most advanced topic in that problem is probably the integral, but even it is trivial if you know the definition of an integral. This is something everyone should know by the time they get out of high school, if not before then.
The toughest computation is the multiplication problem, 65*74 - something we've known how to do since at least third grade.
The rest is simple application of definitions of summations, imaginary numbers, pyth thm, hex, and binary. Again, things people come up on during their formative years in grade and high school.
None of this requires more than a minimum of computational ability. If you know the definitions, you can crunch the numbers in seconds without paper and pencil.
Perhaps Bill was making a point. I think he was trying to parallel the ridiculously easy nature of Sudoku to the ridiculously easy nature of these math problems. If you know how to count from 1-9, you can play sudoku. It requires zero computational ability and zero knowledge of anything in math, history, science, nature, or anything. Just counting. It's why I can't stand this dumb game. After a few times playing it, everyone's an expert. It stops becoming fun almost immediately because after a while, you can do it without even thinking.
Red Viking @ Oct 15th 2006 3:25PM
Sweet! My calculus class IS paying off! I actually knew what the derivative of 3x was!
Liz @ Oct 15th 2006 3:33PM
eialba-
The thing about sudoku is it's a logic puzzle, not a math puzzle. You don't have to have numbers to do a sudoku puzzle, it's all about the symbols. You can use color squares, letters, heiroglyphics - anything. It just so happens that the numbers 1-9 are the most easily recognizable symbols around. It's just a fun logic puzzle. You're taking this way to seriously.
cjr @ Oct 15th 2006 3:49PM
Well, it's true that Sudoku isn't arithmetical - as the comic shows, the numbers are just placeholders. But that doesn't mean it is mathematical. I'm a mathematics undergraduate, and I can testify that I spend a lot more time staring blankly at symbols, wondering what the next logical step is, than I do working with the digits 1-9 :)
Having said that, Sudoku can be reduced down to a few simple logical tricks, so it becomes autonomous at the end. When this happens, do yourself a favour and pick up a book by Martin Gardner :)
Infil @ Oct 15th 2006 4:28PM
No one noticed the "while his sister page questions his actions" typo? His sister's name is Paige. I guess we can attribute another big typo to the medication, eh Ross?
And I agree with eialba, Sudokus are pretty trivial logic puzzles. I believe it's an NP-complete problem for computers, though. At least, I don't know of such a polynomial algorithm.
student @ Oct 15th 2006 4:58PM
Aye, sudoku can be reduced to the Graph coloring problem (that is also seen on maps where each neighboring country must be a different color). You can't allow any one node to have the same color as the nodes it is connected to. To reduce a sudoku puzzle to this problem, imagine each square to be a node, and have each node connected to every other node in the same row, column and 3X3 square.
The thing that I'm most curious about with sudoku is a generator to reduce a blank grid to a problem with one distinct solution. I've found it easy to solve sudoku puzzles but not to create the puzzles themselves.
Ross Miller @ Oct 15th 2006 5:33PM
Aye, page = Paige and that is now fixed.
As for the merits of Sudoku as a game, one could say the same for checkers. Whether or not people think Sudoku is a math or logical puzzle is moot and whether or not it is "tough" is subjective. The mental exercise is still beneficial even if a computer can do it.
If everyone got to the point where Sudoku was a trivial affair, I would have a lot more faith in the universal intelligence of humanity. As it stands, most college students (MIT especially) are not the status quo.
As for whether Amend was making a point, eh, sometimes a joke is just a joke.
Grant @ Oct 15th 2006 5:55PM
Hard Sudoku puzzles can really work your logic circuits, forcing you to think several steps ahead in the chain at times, making you keep track of multiple strands at once. They're not valueless just because they don't make you compute or anything. By the way, try to tell me that this is a simple, valueless exercise: http://www.samurai-sudoku.com/
Moogle @ Oct 15th 2006 6:15PM
Here's a logic puzzle someone pointed me to that is more logic-oriented and entertaining than Sudoku.
http://kaser.com/hotel.html
ReverendGadgetBoy @ Oct 15th 2006 7:35PM
Sodoku? you mean sudoku.
White Rose Duelist @ Oct 15th 2006 7:58PM
If Perplex City hadn't done this first by a year or so, I'd be impressed.
http://perplexcitycardcatalog.com/1/103/
Adam B. @ Oct 15th 2006 10:35PM
Actually, Sudoku is very much mathematical. It comes from tables for symmetric groups for 9 elements. This is taught in discrete mathematics/combinatorics.
Sigma 7 @ Oct 15th 2006 10:36PM
#19:
Easy or "regular" sudoku puzzles are menial, since they are designed in a way where you can identify a location of a number simply because the other cells are directly covered by such a number.
This samauri sudoku is merely five sudokus overlayed. The trick is to attack the corners of the middle sudoku in order to isolate all five sudokus from eachother - once you've done that, you merely have four independant sudokus to solve (in case of the Oct 15, 2006 puzzle, the center one can be solved without having to mark the corner segments.)
If the puzzle isn't hard to begin with, making it larger only makes it longer and/or intimidating rather than more difficult. Hunting down that key to advance the puzzle isn't fun in video games, and isn't fun with sudokus either.
For reference, there's a sudoku solver shown here: http://www.scanraid.com/sudoku.htm
If it solves sudokus without having to enter the naked pairs/triples, then the sudoku was too easy. While you will need to manually enter information inferred from the corners, it solved the center puzzle without issue.
Bob Smith @ Oct 16th 2006 3:27PM
Here's my solution
I'm just a little twisted ... :)
Bob Smith @ Oct 16th 2006 3:29PM
Oops! Where did the link go?
Trying again:
http://img95.imageshack.us/img95/1681/sudorkusolutionvw1.gif
Go Bob! @ Oct 16th 2006 5:29PM
Yeah, Bob's got the right idea! It's more than just solving the expressions -- you have to write new expressions and have 1 type of each expression per row/column/quadrant.
SportWagon @ Oct 18th 2006 3:26PM
Re: FF-F8
> "15*15+15 - 15*15+8 = 15 - 8 = 7"
>
> EEH! Wrong.
>
> It's (15*16^1 + 15*16^0) - (15*16 + 8*15^0)
> = 7
>
> Right answer, wrong method (it's BASED 16, not 15)
They still got 7 because, whatever base you assume, the computation is obviously equivalent to F-8 (since the higher-order digits obviously subtract to give zero). FF-F8 doesn't normally make sense in base 15, or any base less than 16, but the identity will still hold. But for larger bases, the identity holds and makes sense. For instance, you could assume the numbers are base 36 numbers (digits 0..9,A..Z) and FF-F8 will still give 7.
Not sure how someone originally got 3.
I solved the entire thing myself, FWIW.
Joe @ Oct 18th 2006 7:53PM
i don't understand how -(2^.2) is 1 i must be missing something
Ross Miller @ Oct 18th 2006 8:13PM
Joe --
That's actually i, which is a number whose property is i * i = -1
Amy @ Oct 20th 2006 2:01PM
lol ty all...i needed to finish this for a extra credit work 0.0 then i looked it up and i have the answers =D
Dan @ Oct 22nd 2006 8:45PM
So there we were, my wife and I, thinking what kind of dork would try to solve this?
And here we all are...
JWM @ Oct 24th 2006 9:12PM
Actually, post 26, showing a "formulaic" solution, appears to have a mistake. First column, fourth row down, shows "cube root of 492" for 8. Actually, the cube root of 512 is 8. The cube root of 492 is not an integer.
David Baber @ Oct 25th 2006 6:12PM
FF-F8= 1111 1111 - 1111 1000 = 0000 0111 = 7
Bob Smith @ Oct 26th 2006 2:46PM
JWM, you're exactly right. Thanks for catching that!
I was doing some of the math on paper, it was late, and I wasn't thinking clearly. I did 64 * 8 and got 4 * 8 = 12 for some reason (guess I did 4 + 8). So that's 2, carry the 1. 6*8 = 48 + 1 = 49, hence 492.
I can do integrals, but I can't do simple multiplication ... :-P
I'll post a corrected version soon.
Bob Smith @ Oct 26th 2006 3:00PM
Here you go! It's fixed now! (Thanks again!)
http://img262.imageshack.us/img262/1884/sudorkusolutionfixedta4.gif
(The link in my earlier post will still point to the wrong picture, though. No way to edit that ...)
See any other mistakes?