Daley Ponderings

An example (not from this puzzle): "This box can be either a 3 or an 8. If it's a 3, then that box must be a 9, and that box over there must be a 7 -- oops, if that's a 7 then this other box must be a 2, but it can't be a 2, so I've found a contradiction and so the first box can't be a 3." Only in this case it was as if I followed all the logical consequences of the first box being a 3, but never ran into a contradiction. Having actually solved the puzzle, I found my incentive to solve it by a prettier method to be significantly diminished and overwhelmed by my desire to accomplish something else today.

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I choose to solve my sudoku puzzles without guess and check, and if it takes longer i have no problem doing them over the course of a few days. I enjoy seeing if i can find that one clue that will help me solve the entire sudoku puzzle. We all have different ways of solving it and that is fine.

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I didn't think it was very hard -- not even having to use some of the advanced techniques such as x-wing, swordfish, or solving by colors. I learned these solving techniques by downloading "simple sudoku" from internet and going through the demos.

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Yes, if you mean the one I posted, and not the one that sagar linked to.

I have since learned that there are lots of harder suduko puzzles than the ones that typically come in the suduko books and say that they are "hard", it is all relative, I guess.

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Hello all. I am a programmer (both professionally and in my spare time), and I thought it would be a blast to write my own sudoku solver. I just finished it this afternoon and I was in a quest to find the hardest sudoku puzzle. The program uses 3 complex methods to eliminate any invalid solutions in each cell in the process to solve the puzzle. The methods use a system of direct relations, to slightly indirect relations, and to multiple layers of cross examination to finalize any unqiue values, MOST puzzles I let it crunch away are completely solveable with only these three methods. I have found only a handful that require the last reserved method - a recursive method using all remaining permutations until one solves out. This puzzle has no first answer foudn without recursive permutations, which in lamen terms basically means you'd either have to guess the first value, or you were wrong in thinking you found one without guessing. R2C9 (or R1C8 if you count from zero like me) is the first cell from which a solveable permutation is found. If you guess a 9, you'd be in for a long and painful treat. If you guess a 5, then you guessed correctly, From there on out, all values are either directly relational, or indirectly relational without any cross layered eliminations, in other words, fairly easy.

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this was an easy one i have done harder

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I agree the first number is difficult to find, but after it was found, this puzzle fell quickly. I too started with the 3 in the right collumn. The "5-9" pairs in the upper right gave up the location of the 3. Overall this was a fun one...

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MY SUDOKU SYSTEM from Gilbert Kessler, 7/06 New York City Hi -- I only began doing Sudoku two months ago, but as a former math teacher, I started with a book of very difficult puzzles and developed my own system. Since none of the books I’ve recently gotten to look at have it, I’ll call it “Gil’s Dots” and pass it on in the hope that it is helpful to others. It seems to take very little extra time, and has usually (not always) solved the puzzles without requiring “guessing”. Of course, I’ve messed up many puzzles, but always due to carelessness. All the systems put small numbers in squares when you see that only those squares can contain those numbers. In addition, I put small dots or circles next to those numbers as follows: [A] If the number can only appear in exactly two squares of a row, I put a dot to the right of each of the numbers (e.g. 5• -- I hope this looks like a "filled in dot" in this message). This emphasizes that the two choices are in that horizontal row. If I later discover that one of the squares must have a different actual number, the dot immediately directs me to the square where the actual 5 must go. If the number can appear in exactly three squares of a row, I use small circles instead of dots (e.g. 5◦ -- I hope this looks like an "empty circle" in this message!). If I later discover that one of the squares must have a different actual number, I fill in the remaining two circles (thus they become the dots previously described). I do not enter any small numbers that can be in four or more squares. [B] I use the same system when examining columns, but I put the dot or circle just above each small number instead (I put my small numbers in the lower part of each square, so I have room above each number for the dot). This emphasizes that the choices are in that column. It often happens that small numbers have both horizontal and vertical markings. [C] Finally, if I’m examining a (3x3) box and find that a number can only appear in exactly two squares of the box (but those squares are not in the same row or column), I put the dot to the upper right of the number (I can't seem to reproduce this "exponential dot" in this message). That position can later direct me to other squares, but only in that particular box! When there are exactly three choices, I use the small circle instead (e.g. 5˚ -- the circle should look like a "degrees" symbol). In this case, two of the three might be in the same row or column, so you must be very careful about that corner placement of the circle; it directs you to other squares in the box, but does not eliminate possible 5’s elsewhere in the rows or columns. If you eliminate one of those circles later, and the two remaining are in the same row or column, be sure to put in the additional dots (either to the right or above) that indicate this, as that does affect the rest of the row or column. [D] A few general comments (usually using specific numbers for explanation). Several are well known. (1) A major error I find is in not seeing a square that a small number could go in, so using the wrong mark. Also be careful that small circles don’t look like dots and confuse things, and that corner marks don’t look as if they’re in the horizontal or vertical positions instead. Small numbers can have as many as three marks on them. (2) When you enter a small number with horizontal or vertical marks in a single box, that often has implications for the rows or columns of a previously considered box. When entering them anywhere, check if previous entries for that number create an X-Wing or Swordfish (see below). (3) When you discover that a square actually does contain a 5, cross out any other small 5’s in the corresponding row, column, and box. As you cross off small 5’s, their dots often lead you to more squares where actual 5’s must be put. But when you cross off a small 5, if that square contains another small number, be careful not to assume that the square actually gets that other number! (4) If two squares in a single row each contain 5• 6•, then those two squares must specifically contain the 5 and 6 in some order (they “use up” those squares). Any other small numbers in those squares must be eliminated. A similar result is true for a single column (using vertical dots), and for a single box if both numbers have corner dots. (5) The above concept can be extended to three numbers that are within three squares in a row (they “use up” those squares), three that are in a column, or three (even with mixed types of dots and circles) if all are in a single box. (6) A bit of study shows that if four 5’s with horizontal dots occur in squares that are the corners of a rectangle of any size, then you can give each of them a vertical dot also! You can then eliminate any other 5’s in those columns. This is equivalent to the “X-Wing” concept. [An alternate phrasing of this is that if 5’s with horizontal dots occur in two rows, but within the same two columns, each of them can be given a vertical dot also.] The reverse applies if the original 5’s had vertical dots to start with. An X-Wing Explanation: Each row must get one of those 5’s, which eliminates the number 5 from that column; this “spreads” the 5’s into the two columns, so no other 5’s can go into those columns. (7) Similarly, if 5’s with horizontal dots or circles (if there are three) occur in three rows, but within the same three columns, each of them can be given a vertical dot (if there are two vertically) or circle (if there are three vertically) also! You can then eliminate any other 5’s in those columns. This is equivalent to the “Swordfish” concept. The reverse applies if the original 5’s had vertical dots or circles to start with. A Swordfish Explanation: Each row must get one of those 5’s, which eliminates the number 5 from that column; this “spreads” the 5’s into the three columns, so no other 5’s can go into those columns.

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Yes, I do effectively this operation, although I don't use dots. I write the numbers in different corners of the box, and yes, I occasionally get tripped up by crossing out one number, and assuming it has to be the other -- or not really assuming, but just not thinking.
Maybe I will try the dot method, and see if it helps me make less mistakes as my system also does not distinguish very well between 2 or 3 other choices in the same column/row/box. I started out ignoring the numbers with 3 choices, but now I write them down too, and occasionally make mistakes of that order.

As for why you couldn't get the formatting the way you wanted it, you have to use <br /> html tags to get line breaks. I forget now why I changed it, but there was some reason that having my blog code substitute br tags when the commenter typed a carriage return didn't do the right thing.

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.0127 seconds using a python program. well it did take me a few seconds to copy and paste your puzzle into a string in order to pass it to my program. =]

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It must be because python is superior to all other languages, and nothing to do with your coding style...

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my program took 0.38 seconds to complete it. I used php. I thnk 0.38 seconds is quite good for a scripting language..

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Come on, is it really fun to do a puzzle via a program?

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Your solver took 12 seconds when I ran it...

But, I do agree that it can be fun to write programs to solve puzzles - unless you just did a brute force sort of method, which it seems that a 12 second method probably is that.

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My sudokusolver did this one without trial and error (that is without any guessing at all). Hence there is 1 solution only, and the puzzle isnt hard, as i have some that requires up to 10 guesses which i think is the current max of what ive found. (however the number of guesses may be altered slightly by "better" guessing) This is one Sudoku i has turned out to be one of the hardest (got it from another website)

4				3
			6			8
								1
				5			9
	8					6
	7		2
			1		2	7
5		3					4
9

(Solved with 10 guesses in total, 0.6 seconds) This one from the same webpage took 1.2 seconds, but only 9 guesses.

7		8				3
			2		1
5
	4						2	6
3				8
			1				9
	9		6					4
				7		5

Id love to see someone post anything more difficult or if they got a non-guessing solution to these :)