## Killer Book #91

All about puzzles in newspapers, magazines, and books

### Killer Book #91

One of the cages has a total of 26 – meaning that it must contain two identical numbers (9,9,8). On further investigation, the three-number 8 cage towards the bottom left has a total of 8, but won’t accept a 1 in any of the squares, again meaning it must have duplicated numbers: 2,2,4. There is no mention of repeated numbers being allowed and every day the newspaper states " Within each dotted-line "shape", a digit cannot be repeated".

I thought I’d publicize this in case anyone, like me, was assuming that any 8 digit shape must contain a 1. Not the case here.
PaulB

Posts: 6
Joined: 10 October 2005

And there was I thinking the "repeated numbers" issue had been resolved. Interesting and thanks for pointing it out. I've only done a few from the book so far (one from the Times and one from DJApe per day takes up enough time!) - or did you go straight to the "tough" section?
CathyW

Posts: 316
Joined: 20 June 2005

straight to the tough section. i love them, although i can’t do them in stipulated time (need about 50% longer). i can’t do them without writing in candidates either. i ve got a return journey to paris tomorrow, so you know what i ll be doing!

realised after i submitted that of course the 8-digit cage can also be 3,3,2. Key thing is: no 1s, otherwise I guess it could be 1,1,6 as an option.

I’m actually quite cross about all this. I now look at the solutions before i start a puzzle to make sure there are no repeated numbers. I’ve got a bad memory for random numbers so it doesn’t influence the solving process – without knowing how you get there its no fun anayway.
PaulB

Posts: 6
Joined: 10 October 2005

So to clarify, you're saying that puzzle 91 in the The Times Killer Su Doku book has a 3-cell-large cage with a total of 26? I'm highly surprised about this! I assume it must be an L-shape cage overlapping two 3x3 boxes? Shocker!
PaulIQ164

Posts: 533
Joined: 16 July 2005

Or an L-shaped cage overlapping three 3x3 boxes...

Not too surprising to me, when the Times first juggled between the 2 sets of the rules I had the feeling they were gonna create their own puzzles which have duplicates within cages. The Japanese puzzle designers made the "no duplicates within cages" rule in regard to the kakuro/kakro link but there is no such thing as international standard rule for these puzzles (or is there indeed? I'm prepared to be wronged) so the British/Times people should have some freedom to lax this rule and make the puzzles a bit more challenging...

Anyway it's not too bad with a 3-cell L-shaped 26-cage. How about a 3-cell L-shaped 15-cage or a 2x2 20-cage spanning 4 boxes? How many different combinations do we need to consider?
Last edited by udosuk on Mon Oct 10, 2005 2:29 pm, edited 1 time in total.
udosuk

Posts: 2698
Joined: 17 July 2005

Spanning 3 boxes is the same thing as spannign2 boxes really. You can still only have two like digits in the cage, at opposite ends of the L. Otherwise you have two numbers in the same row/column.
PaulIQ164

Posts: 533
Joined: 16 July 2005

Haha I was just pointing out another possibility because you did say this:
PaulIQ164 wrote:I assume it must be an L-shape cage overlapping two 3x3 boxes?

Of course it makes no difference in terms of the number of possible repetitons within the cage (I could see a digit appearing 3 times in a 5-cell W-shaped cage) but in terms of effect to other cells and the whole solving process it could be a different situation. So they are not entirely the "same" thing like you said.
Last edited by udosuk on Mon Oct 10, 2005 2:04 pm, edited 1 time in total.
udosuk

Posts: 2698
Joined: 17 July 2005

Fair point.
PaulIQ164

Posts: 533
Joined: 16 July 2005

thanks for your interesting replies. what annoys me is that they show a 3-digit L box spanning two 3x3 grids in the intro of the book and say that the solution can only be a combination of 1,2 and 3. The logic of the 26 totalling box in puzzle #91 determines that this isn’t the case.
PaulB

Posts: 6
Joined: 10 October 2005

I can see how that would be annoying. And tso won't like it one little bit.
PaulIQ164

Posts: 533
Joined: 16 July 2005

(I could see a digit appearing 3 times in a 5-cell W-shaped cage)

PaulIQ164, I don’t understand this. How can you have 3 repeated numbers in 5 cells. I can’t work it out.[/quote]
PaulB

Posts: 6
Joined: 10 October 2005

Well, it wasn't me that said that, but since you ask, I suppose you could do it like this:

Code: Select all
` ¦ 33¦xx-+--- ¦3  `

Not exactly W-shaped, but there you go.
PaulIQ164

Posts: 533
Joined: 16 July 2005

I didn’t think of that, but then I was thinking of W-shaped or U-shaped, which I think was what was implied. Thanks
PaulB

Posts: 6
Joined: 10 October 2005

(I could see a digit appearing 3 times in a 5-cell W-shaped cage)

I'm the one who said that, and I'll back it up with the following layout:
Code: Select all
`12|--+- 1|2  |1`

But thanks PaulIQ164 for suggesting another 5-cell cage with the same property (which, according to pentomino terms, is F-shaped).

A U-shaped cage couldn't have 3 identical digits because it only has a width of 2. The only possible shapes are F, W & Z.
udosuk

Posts: 2698
Joined: 17 July 2005

Interestingly, no-one seems to have noticed (or at least commented on) the fact that in this very puzzle, Killer #91, there are two '23' triple-box arrangements in the following layout:
Code: Select all
`..........x.......xx............................................x........xx......`

Which of course makes the whole thing completely impossible, duplications notwithstanding.
Karyobin

Posts: 396
Joined: 18 June 2005

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