The New Sudoku Players' Forum

by **GreenLantern** » Sun Oct 23, 2005 5:56 am

I suspect the first Samurai puzzle has multiple solutions but would be
interested to hear from others if it is actually solvable. The furthest I
got was with the center grid which I was able to fill in to the point that
it had 4 possible solutions. Got an answer for A and B but not for C or
D.

by **PaulIQ164** » Sun Oct 23, 2005 12:28 pm

That's about what happened to me. I'll post how far I've got in the central grid:

Code: Select all: 46.¦958¦1.3 19.¦.4.¦5.8 358¦217¦964 ---+---+--- 736¦891¦452 214¦.7.¦689 985¦.2.¦731 ---+---+--- 621¦739¦731 84.¦.6.¦..7 57.¦.8.¦..6

Notice that there's one of those 'unavoidable sets' in 2s and 7s in boxes 1 and 3. In a normal sudoku this couldn't happen, as you could put the 2s and 7s in those 4 squares in two different ways to get valid solutions. In a samurai, though, you can (in theory) work out which way round they go from information in the other grids. As far as I can tell, this must mean that either the top-left grid or top-right grid must now be solveable in isolation, but they're not (I put them into susser). Strange.

by **PaulIQ164** » Sun Oct 23, 2005 12:57 pm

Well, I did some proper scientific investigation. I reckon that this puzzle can't have a uniques solution:

Look at the box where the top-left and central grids overlap (box 9 in top-left grid; box 1 in central grid). There's a 4 and an 8 in it already. Simple elimination means you can place three more numbers, like this:

Code: Select all: 4.. 1.. 358

The 6 in r1c9 of the top-left grid (or the one in r4c3 of the central grid works just as well) restricts the 6 in the box we are considering to being in the central mini-column. This leaves 12 possible ways to fill the remaining 4 cells:

Code: Select all: 62 62 69 67 79 97 27 29 67 69 29 27 92 72 67 69 97 79 92 72 62 62 67 69

Now, a property of Samurai puzzles is that each individual puzzle must be solveable in isolation once the box(es) that it shares with other puzzles are filled in. But I tried the top-left puzzle in Sudoku Susser with each of the twelve possibilities for box 9, and they all either have no solution, or multiple solutions. Therefore, I conclude the puzzle is unsolveable.

If I've made any mistakes here, please point them out. I would love to be proved wrong about this.

by **petef** » Sun Oct 23, 2005 2:43 pm

I agree with PaulIQ164's partial solution and subsequent reasoning.

The central grid has 4 solutions, each of which leave the other grids open.

I picked one of those and completely enumerated 11 solutions for the top left grid. The other three grids had at least one solution.

Thus the number of solutions is at least 11 and probably in the 10s or 100s of thousands.

by **PaulIQ164** » Sun Oct 23, 2005 2:58 pm

So, not looking good for those hoping to win the prize, is it?

by **PaulIQ164** » Sun Oct 23, 2005 3:38 pm

On another note, having sailed through Deadly Killer #64, I'm completely stuck on Tough #63, having only placed 5 numbers (3s in r4c6 and r5c9, 5 in r6c4, 7 in r9c3 and 9 in r9c4).

by **petef** » Sun Oct 23, 2005 4:57 pm

Look at the 22s centre right. Each must contain a 9.

by **PaulIQ164** » Sun Oct 23, 2005 5:10 pm

Very clever. But now I'm stuck again! I placed 9s in r6c6, r1c5, r2c7 and a 7 in r2c6, and can go no further. This is much harder than the adjacent Deadly, to my eye.

Edit: never mind; finished it now.

by **petef** » Sun Oct 23, 2005 5:29 pm

Keep at the 22s. They give you the 13.

by **PaulIQ164** » Sun Oct 23, 2005 7:16 pm

Right. As final confirmation that the page 8 Samurai is bad, here are two possible solutions (I believe there to be many more, but these are one each from the two sets that give different answers to the ABCD cells):

Code: Select all: 927483516 291573468 135672984 685419273 684519273 347682159 712358649 732964581 849126735 459128736 356947821 816735942 573891462958173246895 468235197346528397614 291764358217964851327 736891452 214573689 985624731 394758621739845137296 527961843165297856134 168243579482316492587 716529384 429513768 453186297 653789421 289374156 781264953 971832465 962341875 845617932 534978612 632495718 178625349 A8, B1, C6, D4. --------------------- 927483516 291573468 135672984 685419273 684519273 347682159 712358649 732964581 849126735 459128736 356947821 816735942 573891462958173246895 468235197643528397614 291764358217964851327 736891452 214375689 985426731 394758621739845932176 527361849562317856249 168249573184296417538 786923154 981243765 453186297 653789421 219574386 724561983 971832465 562394817 845617932 439178652 632495718 178625394 A8, B1, C4, D6.

by **dragonandy** » Sun Oct 23, 2005 7:38 pm

That's a relief I thought it was just me.....I got stuck after just half an hour, getting as far as you guys. Then sat back and stared at it for 20 minutes, got bored and did the other two samurai in 40 mins and 55 mins. I hope the Times post a fresh copy of this one. Maybe they made a mistake again like the Championship final Ultra-Fiendish.

by **PaulIQ164** » Sun Oct 23, 2005 7:41 pm

But the Grand Final puzzle as published gave itself away by being asymmetrical. The Samurai, as far as I can see, is perfectly symmetrical. I think it's just a bad puzzle. If you look at the credits on the solutions page, it has a different maker to the other one.

by **PaulIQ164** » Sun Oct 23, 2005 10:28 pm

Sorry to be posting so much in here, but I thought I'd add that as well as the puzzle, The Times' email address seems to be broken too. When I try to send in my solution (such as it is), it just bounces back.

by **Philip Roe** » Mon Oct 24, 2005 11:03 am

Carol Vorderman's analysis of puzzle 89 from the first book of Times puzzles, published in The Times on Saturday 22 October was completely wrong. This puzzle is completely straightforward but Vorderman covered the diagram with wild conjectures. At one point she reached 1-----879/-6-8-7-5-/--7---2--/218756493/---438---/43-921-87/--1---9--/-5-6-9-4-/5-------8 and failed to spot that there is only one place for the 6 in the first row and the 2 in the second. Thus she made an easy puzzle look "fiendish". The odd thing is that The Times has printed this nonsense twice. I hope they didn't pay Vorderman twice.

by **PaulIQ164** » Mon Oct 24, 2005 1:02 pm

Well, I'm going to leap to the defense here. Alright, so the technique wasn't strictly necessary, but it was an entirely valid way of solving the puzzle, and explained to people a technique that will be needed in some other puzzles. If it'd just said "this puzzles really easy", it wouldn't have been much of a guide, would it? And perhaps that's how Carol solved that puzzle. Maybe she saw the thing with the 2s first. Not everyone solves sudoku like a robot.

The New Sudoku Players' Forum

Sudoku Supplement - 22 October

Puzzle 89 First Times book