SudokuSolver Forum

This is really the first greater-than-less-than puzzle I've worked. I get the basic idea (that the arrows point to the lower numbers), but there must be some techniques that are unique to GTLT that I haven't discovered yet.

I don't know of any software that can handle these puzzles, either, so no way of getting any hints. (Unfortunately, even though I can import the candidates into Richard's SudokuSolver and print/save the puzzle, I can't put the arrows in there, much less use the program to solve it.)

This is supposed to be an easy puzzle, but I've made very little headway on it. Here's the puzzle and what I've done so far (along with LCs on 1r2c2/r2c3, 9r7c1/r9c1 and 1r8c8/r9c8). Any ideas on how to proceed?

Plenty of simple eliminations yet to do e.g.

r4c4 = 7/8/9
r1c9 = 6/7/8/9

I would have thought that, after the 1's, the next logical step would be the 9's. (1's are to less-than's as 9's are to greater-than's.)

But no luck. I couldn't find even one 9 to place initially.

So next on the agenda is 2's. 2 can be immediately eliminated from any cell having more than one greater-than coming out of it, or having a greater-than pointing to any cell known not to be a 1.

This immediately eliminates most of the cells in the upper-right box, and forces the 2 in that box to be in the bottom row (r3).

So the 2 in the upper-middle box must be in r1 or r2. All but one of these six cells can be eliminated quickly, forcing a 2 in r2c4.

So then the 2 in the upper-left box must in r1. r1c1 and r1c2 are eliminated quickly, forcing a 2 in r1c3.

That, in turn, forces a 1 in r2c3, and now the rest of the 1's (that were missing from before) can be filled in.

That's as far as I am right now.

Bill Smythe

Bill

Generally raw elimination as you show is the way to get started. However any harder puzzle will require you to find naked or hidden pairs or triplets so for me marking up is necessary.

Cheers

Maurice

PS Note I've made quite a few of these combined with Non-Consecutive - I'll post them if any one is interested.

Whew! I finally solved it.

I postponed all the standard vanilla-Sudoku techniques (singles, doubles, triples) as long as I could, preferring to let the GTLT logic carry the day as far as possible. That's why I like puzzle types I've never tried before. It's refreshing to discover new techniques and stay away from the boredom.

I almost had it yesterday, or so I thought. I had worked it down to four remaining cells, which formed a "deadly non-uniqueness rectangle", i.e. four cells at the corners of a rectangle all of which could be either of two values. At first I thought, aha, I've cooked the puzzle. But I went back and checked everything just to be sure. I found everything to be in compliance with all vanilla Sudoku rules. I then checked the GTLT's, and lo and behold, there was one error. (And it was nowhere near the deadly rectangle.)

Knowing from experience that this kind of error can seldom be corrected by a handful of switcheroos, I started over with a fresh copy of the puzzle, setting aside the original copy so I wouldn't again fall into whatever error I had made the first time. This time I found the correct solution.

Then, comparing my second solution with my first near-solution, I found my first version to be incorrect in over 30 of the 81 cells! Usually, when a puzzle goes south, it's because of an error within the last 10 or so moves. I never expected to find a solution that was correct to within a uniqueness rectangle except for one error elsewhere. Yikes!

So, Hatman, I hereby issue the following challenge. Figure out what my original near-solution was. Find a "solution" that obeys all the vanilla Sudoku rules, but differs from the correct solution in at least 30 cells, and has exactly one non-uniqueness rectangle and exactly one GTLT error.

Bill Smythe

After I posted, I reprinted my puzzle progress (helps to make some of the pencil marks less obscure). Then I started noticing chains of greater-than (> > > >) and less-than (< < < <), and found quite a few eliminations that way. I haven't yet had time since then to complete the puzzle, but I think I'm on my way.

Bill

Interesting outcome - however I do not have enough life left to solve that problem - it reminds me of the problem of parameter estimation.

State Estimation: In power systems you have transmission line parameters together with multiple redundant meter readings with errors (these are assumed to be normal distributions - with some being totally bad {telemetry problems etc.}). You then perform a flow analysis together with an error minimisation analysis (normally least square) to find the "true" meter readings and the state of the power system.

In 1984 in China Light and Power (Hong Kong) we put in our first state estimator and the first job I did was to check that our transmission line parameters were correct. Given that the number of states is less that the number of parameters this problem is somewhat difficult. The solution was to repeat the process many times at different times of day with different generation and demand patterns.

I found some significant errors and the process took me four months. Note this was in an orderly Chinese/British environment. Here in Nigeria we are just putting in our remote supervisory system and in the next couple of years we will need to get the state estimator working. As you can imagine the data here is in a complete and total mess, so I have no idea if it is doable never mind how long it will take.

All-in-all I will not be taking up your challenge.

Cheers

Maurice

Finished it! Once I got going with the GT chains and LT chains, it was just a matter of time. I think those chains are of far more importance to these puzzles than the usual sudoku techniques. As a matter of fact, as far as standard sudoku techniques, this puzzle requires nothing more difficult than locked candidates.

I was afraid that might be your response.

Gee, are you sure that wouldn't make an interesting program to write? All it'd have to do is generate all possible GTLT puzzles, then check them one by one.

Bill Smythe

Bill, you are truly evil.