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Posted by Sue 
January 27, 2013 10:19AM
Hello Christine, Marilyn (and any other inequalities obsessives)

Agree it is time this topic had its own thread so here it is!

For those new to this, the 3 of us have been sharing our frustrations, tips and hard won successes in the 200 thread whist trying to crack the maddeningly difficult, but fantastically satisfying, inequalities puzzles in Gareth's Sudoku 200 series. A brilliant book for those who like a challenge. Do join us. We need all the help and encouragement we can get.

Christine, so glad you are getting there now and have joined Marilyn and I on this quest. I am still trying to crack the unfinished ones that I have abandoned down the line with slightly more success. This should indicate that I have found some previously hidden logic but sadly not. Like you I always start with 9's and 1's followed by 2'' and 8's and then see where i am at.

I think I am getting better at following long chains and considering all the possible numbers that fit, even if there are 3 or 4 (occasionally) options. Sometimes this throws some light on other cells in the lines, columns and boxes. For example, if I know that a cell can only contain a 3 or a 4 then a chain in the same line cannot contain both the 3 and 4. Does that make sense? In other variants I do not usually bother if there are more than 2 options but these call for greater analysis. However, even doing this, the puzzles still take a long time and often several visits to complete (if then!). If still not there I rub out all my "possibles" and leave it for a bit. Hence all the embarrassing gaps in my book.

I have now attempted most of the puzzles upto 132..... this is now the only book I seem to pick up! I have completed almost exactly half of these so not overly great. Of recent new ones I have tried, no 129 worked out on first attempt although i wouldn't say it was easy. But then none are. That might sound good but I am STILL stuck on no 14 (see earlier posts).

And has anyone done 21? I keep going back to it but so far have not managed to place one number! What am I missing? It's windy and raining where I am today so might find some time to try again....


Looking forward to some comments, inspiration and any tips!

Gareth, if youre reading, these are the best!
Re: Inequalities
February 02, 2013 04:14AM
Yes, inequalities are most deserving of its own thread! Thanks for starting it, Sue!

Christine, I shall make a note of easier ones for you. Thinking back, I remember 1, 5, 12 & 14 being particularly tough. Of the earlier puzzles, I do remember saying "that was a nice one" a few times. I think 6 & 7, 10? I'm currently up to 29, so between 20-29, 20, 23 & 24 were the easiest, 22, 25-28 ok.

As to 21 - nope. Sorry, Sue! This puzzle broke my rule of finishing one puzzle before starting another. All I had for it were two of the 9s in fixed locations (box 1 and box 5). After a couple of days of nada, I was desperate to move on! I keep going back for another crack at 21. I've erased the pencil marks a few times, put them back in one at a time with careful scanning, studied the chains and combinations but I can't progress. I keep fixating on the chains in boxes 6 and 9 and how they affect each other in various combinations, but have only managed to eliminate one number from the equation, a six in cell 5, box 6. Let's shout together, "what are we missing?"!!

My preference with these puzzles is to start with the 9s. If I get some of those and/or fixed locations, I then do the 8s, and work down. If nothing much is forthcoming, I start on the 1s and 2s. Most puzzles give a starter at one end or the other, but I’ve been lucky enough to find longer runs working down from the 9s, than up. Sometimes it’s even, sometimes you get more from the 1s up. Some puzzles don’t yield much at all and it becomes a matter of deeper deliberation of the rows, columns, boxes, chains. Usually I can find a straggler or two in the grid, where I’ve eliminated pencil marks and left highest/lowest numbers pointing to itself, or I’ve accidentally duplicated a given. I find it helps to rub out the remaining possibles, once you have a good amount of numbers and looking at it like a normal Sudoku. I've finished a few puzzles doing that, where previously my attention was drawn too much to the jumble of possibles.

I wish I could say I had a leap of logic with the puzzles I’ve completed, but I’ve put that down to the luck of longish runs, fewer possibles to write in and tidying up. It’s rare that I finish a puzzle in one sitting. Usually I do the groundwork – get as many numbers as I can, put in the possibles, then have a rest. If I’m on a roll, I’ll continue. So far, 23 and 24 were great for getting in one sitting. Hmn, now that I've broken my rule, I might have a go at 129!!

I have composed a song to keep us motivated with the toughest ones. I think I'll dedicate it to 21.

Ready to sing along? It's to the tune of "You'll never walk alone"

"When you struggle with an inequality, give it a prod and declare
'I won't be defeated by you.
Amongst all those possibles and arrows,
I’ll find you somewhere,
Oh sweet, silver glimmer of a clue.'
Strive on, though you're eyes are crossing,
Strive on, though your brain cells are frying,
And know you are not struggling alone,
You are not struggling alone"
Re: Inequalities
February 04, 2013 02:51PM
Hi Marilyn

Loved the song, although the tune does have other connotations for we sad football fans! I have just been going back through the abandoned puzzles AGAIN deleting all the possibles, not for the first time with some of them. Over the last week or so I have managed to complete all the puzzles on page 34 which is quite satisfying. Also 137 (at first attempt), 139, 141 and 142. I occasionally feel I am getting a little better at them.... however as soon as I dare think that I get stuck again! Do let me know your continuing progress. I am trying to resist turning to a fresh page before i have filled my many gaps. We appear to be using the same strategies, but you seem to have cracked some that are still bugging me so well done to you. I applaud your persistence.

Interesting that you haven't managed to make any headway with no 21 either. Gareth, if you are reading, perhaps you could give us a clue? Something about these we are missing perhaps?

Meanwhile, I am enjoying the Non-consecutive diagonals in Issue 22 for a break. Excellent puzzles.

Re: Inequalities
February 04, 2013 03:26PM
Puzzle 21? I'll print a copy and take a look. smiling smiley
Re: Inequalities
February 04, 2013 03:38PM
Okay, so I start this puzzle by writing in the minimum value in each cell.

Having done that I see immediately that there's an x-wing on the 1s in row 4 and row 8. This lets you eliminate all other 1s in their columns, 4 and 7.

This means you know the 1s must be in the middle row of the top-middle 3x3, eliminating them from elsewhere on that row.

You can now place a definite 1 in the top-right 3x3.

Without going any further, I imagine that helps?
Re: Inequalities
February 04, 2013 03:41PM
And just in case it's not obvious, you can then immediately place all of the other 1s.

Edited 1 time(s). Last edit at 02/04/2013 03:44PM by gareth.
Re: Inequalities
February 04, 2013 03:46PM
Next up, 2s must be in the top row of the top-middle 3x3, and right column of the top-right 3x3. And better still, there's only one place in the 6th column where a 2 can now fit.

Edited 1 time(s). Last edit at 02/04/2013 03:46PM by gareth.
Re: Inequalities
February 04, 2013 03:47PM
And only one place in the middle-left 3x3 where a 2 can fit.
Re: Inequalities
February 04, 2013 03:48PM
And only one place in the 4th row where a 2 can fit.
Re: Inequalities
February 04, 2013 03:49PM
And now only one place for a 2 in the bottom-right 3x3.
Re: Inequalities
February 04, 2013 03:50PM
Which means the 2s must be in the top row of the bottom-left 3x3, letting you place a 2 in the bottom-middle 3x3.
Re: Inequalities
February 04, 2013 03:51PM
Now you can place the 2 in the top-middle 3x3, so at this point you should have 9x1 and 6x2 placed, and all I've written in the grid so far is the minimum number that can fit in each cell (which I've updated as at each step one gets forced higher by a placement).
Re: Inequalities
February 04, 2013 09:54PM
Thank you Gareth. I now know what an Xwing is! I had not spotted that pattern in all the mess I had made. You are right of course and have now placed all the 1's quite quickly. I will try to complete the whole puzzle now and will only study your other tips if I get stuck again.

Thank you for such a detailed response. I am really enjoying these puzzles and with your tip I might be more successful from now.

Re: Inequalities
February 04, 2013 10:00PM
PS Gareth, do you always start these by putting in the min value of each cell? Never thought of doing this. Is that how the experts start then?

I usually start looking for a 1 or a 9 to place and work on from there with variable results as you may have seen!
Re: Inequalities
February 04, 2013 11:25PM
I don't claim to be expert at solving inequalities quickly, but yes that's what I do first. I go as far as I can with the minimums, then when I get stuck I repeat with the maximums. As long as possible I avoid writing in any other candidates, because it makes it really hard to see the wood for the trees. smiling smiley

I think to be fair you'd find these puzzles easier if they were two to a page and you had more room for neat pencil marks. I printed mine twice as big, and it definitely helps me! smiling smiley
Re: Inequalities
February 05, 2013 03:58AM
Many thanks for your input, Gareth!

I've not thought of putting in the minimum values for each cell, either. I am quite excited about trying a new method and will retackle 21 tomorrow.

I rarely think of the more advanced techniques, so this'll be great for practicing an X-wing!

Sue, Christine, I hope you get to finish gaps now and progress further.
Re: Inequalities
February 05, 2013 09:20AM
Hurray! After weeks of frustration I have now completed puzzle 21 just starting with the Xwing. I didnt put all the minimums in as suggested but will try another puzzle like that today. It worked out relatively quickly once started. Very satisfying to have finally cracked it.

Thank you for the tips Gareth. I might print the ones in issue 22 double size and see if that helps as you say. I am so pleased to have these puzzles back in Xtra. They disappeared for several issues and I missed them. The 200 book is terrific. Thank you. I would love another one sometime (but not yet!!). I hope they are selling well for you. I did write a review on Amazon as requested.
Re: Inequalities
February 05, 2013 08:24PM
Hi Marilyn, Sue and Gareth

First of all Marilyn - your song really made me smile! Shows how much the puzzles must have inspired you if you are composing songs to help!

Sue, congratulations on finally completing 21. I am really impressed by yours and Marilyn's brain power and determination! My progress is much slower (probably doesn't help that I don't know what an X-wing is - can you solve the puzzles without knowing that?). I am pleased to report one small success though. I have completed another one - number 24, and I have made a note of the puzzle numbers that you have both mentioned are slightly easier and will have a go at those next.

Gareth - great idea to print the puzzles out larger and also just start with the minimum number for each cell. I will try those two things now.

I think that "glutton for punishment" may be the best words to describe me - all of us for that matter, because even though I have bought another four of the 200 series, all of which I find much easier to solve, I keep going back and back to the inequalities waiting for the 'Eureka' moment!
Re: Inequalities
February 05, 2013 09:08PM
"(probably doesn't help that I don't know what an X-wing is - can you solve the puzzles without knowing that?)"

In many cases, nope. smiling smiley

It's a funny name but an easy piece of logic so you probably sometimes apply an equivalent deduction without calling it an x-wing. They're not always easy to see though.

The x-wing deduction (which has nothing to do with 'x's - "square deduction" would be more accurate) is that if there are only two locations for a candidate in a row, and only two locations for that same candidate in a different row AND both of these two locations are in the same two columns THEN you can remove that candidate as a possibility from all other cells in those two columns. (And then the same logic with row and column exchanged throughout, of course)

Think of it like a hash symbol: #. If you have the candidates on the intersections of the lines and those are the only candidates in a pair of rows or columns, you can eliminate them from the intersecting lines.

My inequalities (including Futoshiki) use this deduction a lot to get started.
Re: Inequalities
February 06, 2013 01:53AM
Well done, Sue! I'm doing a happy dance with 21 solved, as well! I started just with the 1s to get a look at the x-wing, then put in the minimum values to get a feel of working a puzzle that way. I really like that method as it's a lot tidier.

Christine, you will keep going back to the inequalities, oh yes! One minute you're happily doing puzzles from all the other books, then suddenly inequalities have crept up, sunk their teeth in and won't let go! With these new methods, I think I'm even more addicted now, if that's possible, but loving every moment. Thanks, Gareth!
Re: Inequalities
February 06, 2013 07:24AM
Thanks for that explanation Gareth. It seems I have been using that piece of logic without realising it was called an x-wing. I think the best thing for me is to enlarge the grids so that I can see all the pencil marks more clearly! I'm not giving up!!!

Well done Marilyn on cracking number 21 - I think I'll leave that one for a bit and work my way up to it!
Re: Inequalities
February 06, 2013 09:43AM
Christine, I am really pleased Gareth has explained the X wing thing for you. I was pondering how to put it into words. Needs a diagram really which is tricky in a comments space. I did not know that term either although I have been using the logic over the years. I am enjoying thinking that the name drives from the X fighters in Star Wars. It's great music to have in your head for that lovely moment when you place a key number and the puzzle suddenly unravels! I find it very usueful technique but quite hard to spot sometimes, particularly when you have a lot of "possibles" pencilled in and the X rows are far apart.

Like you I keep coming back to these. Other variants seem quite easy now by comparison and far less satisfying as a result. Oh dear.... what next I wonder?

Marilyn, I am pleased you have solved No 21 as well *punches the air*!! I am so glad we started this thread and Gareth joined in to help us. I feel newly energised and yesterday evening manged to complete 6, yes SIX, puzzles. That must be some sort of record, for me at least. I opened a page of unfinished/unstarted ones at random and off I went. Pages 32/33. I did all bar 123 and 124 which I shall try today, and completed them all (slowly) at first attempt. Definitely a breakthrough. I haven't used Gareths method successfully yet but something has clicked in my brain (or maybe this puzzles were slightly easier - hard to tell really).

Gareth, thank you again for joining in. A great help. Do you have any suggestions for our next tough challenge? I am thinking maybe Jigsaw Extra Regions which I also find very hard. I would be interested to hear which variants you consider the most challenging.
Re: Inequalities
February 07, 2013 07:19AM
Six puzzles in one evening Sue - I'm impressed! I was feeling pleased with myself this evening when I did two! I managed number 44 in one sitting - that one was quite straightforward in the end (still took me an age mind!) and I also completed 113 which I had previously started and got stuck on. It's definitely inspiring me having you and Marilyn to discuss successes with!!
Re: Inequalities
February 08, 2013 08:17AM
Hi Christine

Yes I it is definitely encouraging to be chatting with other puzzlers on these tricky ones. Sounds like you are making good progress now. My bubble burst after my inspired 6 evening but it gave me the confidence that i might one day complete the book. Not any time soon tho. I have found looking for "Xwings" in puzzles I had abandoned has been quite successful but not every time unfortunately.

Keep at it!!
Re: Inequalities
February 09, 2013 02:20AM
6 puzzles in one evening! Wow, that is some achievement, Sue! Have you cracked 14 yet?

Christine, congratulations on your successes. Sounds like you've found your mojo!

I'm enjoying using the minimum value method. I've found it's helping to cure my habit of leaving stragglers. I'm not 100% yet, but getting there! I'm not too good at spotting X-wings unless they are at the beginning. In the few puzzles I've done since finishing 21, I found 2 X-wings in the early stages and that was fun, in 35 and 36. 33 is giving me grief, so if an X-wing is lurking there I can't find it. I'm a lot more relaxed in my rule of finishing the puzzles in order, but I do try to finish a page before turning over! So currently I am on page 10, bouncing around 33, 34 and 35, with 36 finished.

I might have to put my book away for a while or otherwise spend not so much time with itsad smiley Hitting a busy period at work that might require long hours in the office and some weekend working. If that happens I'll take one of the easier books to work on while travelling so as not to be totally devoid of puzzles.smiling smiley
Re: Inequalities
February 19, 2013 03:38PM
Hello again

6 in an evening was a definite one-off but progress is still being made over here. I have filled in some of my gaps and try hard to resist turning to a new page but the temptation to try a virgin puzzle is too much sometimes. I am now completed about 95 puzzles and am into the 160's, so still plenty of gaps to fill, and trying to slow down as I near the end of the book. The trouble is, I now find the puzzles in the other books or Xtra much less satisfying which is rather disappointing really. I quickly get bored and turn yet again inequalities.

I am going to need a new book or a new challenge by Easter I think. Any suggestions?

In the meantime, if you need a confidence boost, I completed 155 in record time last week. Not sure if I was feeling unusually inspired or it is slightly easier. Either way I was delighted. Still not finished 14 tho!!

Keep X winging folks....
Re: Inequalities
February 19, 2013 09:29PM
My busy work period has not transpired yet, so still puzzling and about to start page 13.

Christine, of the latest batch (33-44), easy ones I've marked are 38, 39, 40, 41 and 43. The others were toughish, with 33 being quite hard. I made a complete dogs dinner of 44.

Sue, I wish the compulsion to do inequalities could be explained. I haven't done any puzzles in Xtra 22 yet. I really want to do the 13-grid consecutive puzzle, but go right back to the inequalities! Not sure what to suggest for you. Do you have any of the 101 Samurai books? I've got 6 of them, star, jigsaw, 13-grid, arrow, outside and standard samurai. Challenging in their own right, with jigsaw and star being the most challenging. I haven't started the arrow book yet as I can't get my head around them in the 200 series!

In the 200 hundred series, the kropki and jigsaws would be the most challenging for me (and arrow). I now have 12 books in the 200 series, LOL, with the 3 Futoshiki books having just arrived, LOL. The Sudoku Xtra Specials 100 Consecutive Sudoku book is challenging, too.

Who knows, by Easter there may be an Inequalities Book 2. I hope so, I hope not! I want to go back to the other books and see if the minimum/maximum values work for other puzzles, but I can't because I keep hearing the call of an inequality.

I'm off to answer that call now.

Happy puzzling, everyone!
Re: Inequalities
February 21, 2013 12:32PM
Thank you for the suggestions Marilyn. I have some of the books you mentioned and occasionally dip into them but none of them have really grabbed me yet. Enjoyable, yes, but not as challenging really so I slink back to this one. I now find my unfinished ones are so messy I can't face them yet again so I am going to make a fresh start on them with a brand new book. Another sale for you Gareth!

Of the Xtra variants I find the Extra Region Jigsaws really challenging and tricky so maybe if we ask nicely we might get a book of them maybe. Also an Inequalities 2 would be bought in an instant!! I hope the first one sold well enough to justify the effort of producing a new one. A Samurai (Star) Inequality would be fantastic too.

Gareth ...... are you listening???

I cannot believe I have spent nearly 3 months on this book already and still less than 75% solved. However, I do seem to be getting more successful as I progress through the book. Generally speaking I can now usually complete 2/3 per page at first (very slow!) attempt. A considerable improvement since the early days and encouraging. It is still always immensely satisfying to finish one.
Re: Inequalities
February 21, 2013 08:53PM
Sue, must agree with you on those new book ideas, pretty please, Gareth!

Sue, it really urked me that I made a dog's dinner of puzzle 44 and put a cross through it. My first thought was to order a second copy of the book immediately! I was going to order another copy when I finished this book, anyway, assuming a book 2 doesn't emerge, but I can't be having puzzles crossed out. No, no, no, no! Then I had an idea for the interim. I created a sudoku grid using the Tables function in Word, printed a few out and re-did 44. I had to be careful to draw the arrows in correctly, though!

Then I did puzzle 14 again. I remember having a hard time the first time round, cracking the puzzle eventually, somehow. I wanted to see if I could get in that stuck situation again and what I did to get out of it and maybe give you a clue. This time round, I started with the minimum and maximum values. I couldn't spot any x-wings, niether did I get stuck! Although it took a while, I breezed through it easier than the first time.
Maybe you could try redrawing the puzzle, or using the minimum/maximum method when you get your new book!

I've had my book for a little over 2 months, and only on page 13! You have done remarkably well, Sue.
Re: Inequalities
February 22, 2013 09:38AM
Hi Sue and Marilyn - glad to hear you are still continuing to do so well with the puzzles. Sue - you are making just amazing progress.
Marilyn - thanks for pointing out some of the easier ones for me - I have put an asterisk by those puzzles and will have a go at them next. At the moment I seem to be going through the book and trying out puzzles at random. Strangely enough, puzzle 44 was one of the ones I actually got in one sitting, so one small triumph for me at least. I am still finding them very hard going in general and spend ages sitting and getting nowhere fast. It doesn't put me off trying - I am finding them fascinating, but I think there may come a time when I will say enough is enough! (Though just when I am getting to that stage I finally manage to crack another and it keeps me plodding on).

I have about 6 of the 200 series - the XV are actually quite easy (how nice to be able to say that - they make a bit of much needed light relief sometimes) - mind you I have the second half of the book to go yet so presumably they will get more difficult.
I'm really enjoying the Kropki although I have to be in the right frame of mind to get started, also the arrow sudoku which I am finding ok so far.
One of my real favourites at the moment is the Mystery Killer Sudoku Pro - so far quite a challenge but still manageable!

I probably would buy a second Inequalities book though I would prefer them to be a bit easier (not sure you two would agree with that one!)

What I would really like would be a book of skyscraper sudoku puzzles (more interesting than the plain skyscrapers) and a book of mixed samuai variants - Gareth we are rather a demanding lot aren't we?!! Really enjoying your puzzles, thank you!

I know it's not maths, but how I used to hate maths at school and had to work really hard to get my maths GCSE whereas literacy subjects came much easier - yet these days I'm not a bit interested in word puzzles - just want to play around with numbers all the time!
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