## Sudoku Supplement - 22 October

All about puzzles in newspapers, magazines, and books
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.

GreenLantern

Posts: 26
Joined: 19 August 2005

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

Code: Select all
`46.¦958¦1.319.¦.4.¦5.8358¦217¦964---+---+---736¦891¦452214¦.7.¦689985¦.2.¦731---+---+---621¦739¦73184.¦.6.¦..757.¦.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.
PaulIQ164

Posts: 533
Joined: 16 July 2005

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  6779  97  27  2967  69  29  2792  72  67  6997  79  92  7262  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.

PaulIQ164

Posts: 533
Joined: 16 July 2005

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.
Last edited by petef on Sun Oct 23, 2005 2:02 pm, edited 1 time in total.
petef

Posts: 30
Joined: 17 May 2005

So, not looking good for those hoping to win the prize, is it?
PaulIQ164

Posts: 533
Joined: 16 July 2005

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).
PaulIQ164

Posts: 533
Joined: 16 July 2005

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

Posts: 30
Joined: 17 May 2005

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.
Last edited by PaulIQ164 on Sun Oct 23, 2005 1:31 pm, edited 1 time in total.
PaulIQ164

Posts: 533
Joined: 16 July 2005

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

Posts: 30
Joined: 17 May 2005

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   291573468135672984   685419273684519273   347682159712358649   732964581849126735   459128736356947821   816735942573891462958173246895468235197346528397614291764358217964851327      736891452      214573689      985624731394758621739845137296527961843165297856134168243579482316492587716529384   429513768453186297   653789421289374156   781264953971832465   962341875845617932   534978612632495718   178625349A8, B1, C6, D4.---------------------927483516   291573468135672984   685419273684519273   347682159712358649   732964581849126735   459128736356947821   816735942573891462958173246895468235197643528397614291764358217964851327      736891452      214375689      985426731394758621739845932176527361849562317856249168249573184296417538786923154   981243765453186297   653789421219574386   724561983971832465   562394817845617932   439178652632495718   178625394A8, B1, C4, D6.`
PaulIQ164

Posts: 533
Joined: 16 July 2005

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.
dragonandy

Posts: 1
Joined: 23 October 2005

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.
PaulIQ164

Posts: 533
Joined: 16 July 2005

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.
PaulIQ164

Posts: 533
Joined: 16 July 2005

### Puzzle 89 First Times book

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.
Philip Roe

Posts: 12
Joined: 24 October 2005

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.
PaulIQ164

Posts: 533
Joined: 16 July 2005

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