I solved it by finding a hidden pair (12) in one of the rows and then a hidden quadruplet (2345) in one of the columns (I think).

Here are a couple of more general Futoshiki techniques: * If you have a square which you know is either 1 or 2, and somewhere else in the row/column there is an X < Y, then Y cannot be 2 - otherwise it would force X to be 1 and there would be no possibilities left for the first square. The same thing works with other consecutive numbers, and not just pairs either! * If you have X < Y > Z in the same row or column then Y cannot be 2, as it would force X and Z to both be 1. In general, Y must be at least 2 greater than both X and Z. The same sort of thing works with X > Y < Z and longer chains of inequalities.

Posted 5th Feb 2019 at 16:33

Elisabeth Daily subscriber Rated puzzle: Hard Completion time: 53:17

Yes, Pseudo, I found those too,eventually! But it wasn't an easy one, partly with the difficulty of looking up/down columns, left/right rows in a grid that seems much larger than the standard 9x9 suduko!!

Posted 5th Feb 2019 at 19:08 Last edited by gareth 5th Feb 2019 at 23:06

(yes, I gave in, I subscribed, I was curious)... Here is an image that shows what Pseudo is talking about (I cut the left third of the puzzle): http://joergwausw.de/PM/Futo8-223.jpg

The important square is the shaded one.

Hidden pair: In row 4, the two green boxes show that only 1 and 2 are possible, because they are nowhere else in this row. This is why the shaded square has to be 1 or 2 (making the square above the 8).

First general technique: All the numbers in red squares can be eliminated, because if those were correct, the > relations would force the smaller squares to have 1 AND 2 in them - nothing left for the shaded square.

Second general technique (I forgot to mark these): - Third row, first shown square (678): No 5 here, because the two lower than-sqares above and below can't be both 4. - Second square in this row (234): No 5, because the two adjacent greater than-squares can't be both 6. - Test question: second row, first square: what number can be eliminated? - Advanced test question: Two sqares below the 1 (second from the bottom, second from the right, containing 4567) - why can the 4 be eliminated?

Hope that helps...

Posted 5th Feb 2019 at 23:07 Last edited by gareth 5th Feb 2019 at 23:10

gareth Administrator Daily subscriber Has started but not yet finished this puzzle

I just edited JoergWausW's comment to turn the link into a clickable link, but what an incredibly helpful comment - thanks!

Posted 6th Feb 2019 at 00:00

purrs Daily subscriber Completion time: 9:49 Used 'valid marks' Used 'auto remove' Used 'show wrong moves'

I know the tricks, there's just so much going on that I can't *find* what I need to use the tricks on. I get about this far and then to get any farther I just brute-force guess and check.

purrs: In column 5 there's only one square where the 8 can be.

Some other solving tips:

If there are no starting numbers given, then the first numbers you're going to be able to solve will be 1 or N (where N is 8 in this puzzle). So for the first few minutes all you need to do is scan across rows and columns trying to solve for those two numbers.

If you don't have any clues on the candidates for a particular square, leave it blank until you do. In other words, don't fill it in as 12345678 - wait until there's a number to eliminate. That makes it a bit easier to spot interesting squares. In this puzzle, it doesn't really help with that 8 in the fifth column but it makes it easier to find the "hidden" 12 pair in row 4: https://imgur.com/fOLzWh5

I don't leave squares without clues blank - because I "fortget" that they contain all numbers, especially if there is only one blank square in a row or column. In Pseudos Screenshot I might accidentally put the 8 in 5th column 3rd row, because I don't see any other 8 in that column. That will turn out to be correct in the end, but shouldn't happen at this point. On the other hand in this version it is easier to spot the hidden pair in 4th row. And it saves a little bit of time.

So in the end it's everyone's own choice whether to leave those squares empty or not.

@gareth: Thanks for the linkable edit. This puzzle just happens to show a lot on little room...

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Add new comment)9:49Used 'valid marks' Used 'auto remove' Used 'show wrong moves'ModerateCompletion time:14:58Used 'remove'Here are a couple of more general Futoshiki techniques:

* If you have a square which you know is either 1 or 2, and somewhere else in the row/column there is an X < Y, then Y cannot be 2 - otherwise it would force X to be 1 and there would be no possibilities left for the first square. The same thing works with other consecutive numbers, and not just pairs either!

* If you have X < Y > Z in the same row or column then Y cannot be 2, as it would force X and Z to both be 1. In general, Y must be at least 2 greater than both X and Z. The same sort of thing works with X > Y < Z and longer chains of inequalities.

HardCompletion time:53:17Last edited by gareth 5th Feb 2019 at 23:0643:34Here is an image that shows what Pseudo is talking about (I cut the left third of the puzzle):

http://joergwausw.de/PM/Futo8-223.jpg

The important square is the shaded one.

Hidden pair: In row 4, the two green boxes show that only 1 and 2 are possible, because they are nowhere else in this row.

This is why the shaded square has to be 1 or 2 (making the square above the 8).

First general technique:

All the numbers in red squares can be eliminated, because if those were correct, the > relations would force the smaller squares to have 1 AND 2 in them - nothing left for the shaded square.

Second general technique (I forgot to mark these):

- Third row, first shown square (678): No 5 here, because the two lower than-sqares above and below can't be both 4.

- Second square in this row (234): No 5, because the two adjacent greater than-squares can't be both 6.

- Test question: second row, first square: what number can be eliminated?

- Advanced test question: Two sqares below the 1 (second from the bottom, second from the right, containing 4567) - why can the 4 be eliminated?

Hope that helps...

Last edited by gareth 5th Feb 2019 at 23:109:49Used 'valid marks' Used 'auto remove' Used 'show wrong moves'http://oi65.tinypic.com/nzhizm.jpg

ModerateCompletion time:14:58Used 'remove'Some other solving tips:

If there are no starting numbers given, then the first numbers you're going to be able to solve will be 1 or N (where N is 8 in this puzzle). So for the first few minutes all you need to do is scan across rows and columns trying to solve for those two numbers.

If you don't have any clues on the candidates for a particular square, leave it blank until you do. In other words, don't fill it in as 12345678 - wait until there's a number to eliminate. That makes it a bit easier to spot interesting squares. In this puzzle, it doesn't really help with that 8 in the fifth column but it makes it easier to find the "hidden" 12 pair in row 4: https://imgur.com/fOLzWh5

43:34In Pseudos Screenshot I might accidentally put the 8 in 5th column 3rd row, because I don't see any other 8 in that column. That will turn out to be correct in the end, but shouldn't happen at this point.

On the other hand in this version it is easier to spot the hidden pair in 4th row. And it saves a little bit of time.

So in the end it's everyone's own choice whether to leave those squares empty or not.

@gareth: Thanks for the linkable edit. This puzzle just happens to show a lot on little room...

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