Magic Hexagon Killer

For fans of Killer Sudoku, Samurai Sudoku and other variants

Magic Hexagon Killer

Postby udosuk » Thu Jul 03, 2008 10:33 am

Image

I hope the pic (and the title) is self-explanatory enough. If you still need extra help then try googling the first 2 words of the title.:idea:

However, even after you've fill in the cage sums, the average killer players might still find it a bit too "Ruudiculous" to solve. No problem, I've provided some letter-shaped gadgets for all levels of players.:)

Firstly, with a "T" it can become more solvable but still a Tough nut to crack:

"T" version

Then, with a "V" it's not so tough but still Very challenging:

"V" version

If still too hard, with an "M" it will become a Medium level puzzle:

"M" version

Well if that's still not easy enough, I'll throw in a "Y" to make it "Yeasy peasy"::D

"Y" version

Enjoy!:)
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby Bigtone53 » Thu Jul 03, 2008 3:03 pm

Nice one, udosuk.

I guess that the basic decision is which way to 'flip' the chart having put in the 19 - 5 - 14 diagonal, but sadly, either way led me to a contradiction:( . It is obviously me who has messed up but I am too proud to go for the hints.:( again.
Bigtone53
 
Posts: 413
Joined: 19 September 2005

Postby udosuk » Thu Jul 03, 2008 3:56 pm

Bigtone53 wrote:I guess that the basic decision is which way to 'flip' the chart having put in the 19 - 5 - 14 diagonal, ...

That's a great observation.:) I suggest you to try again as one of the way should be very easy to eliminate. You probably made a careless mistake when you found both of them leading to contradiction.:idea:

Afterwards if you plan to solve the killer I suggest you to try the easier versions first, from the bottom up (i.e. the "Y" version).:idea:
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby Bigtone53 » Fri Jul 04, 2008 3:18 pm

OK, will do, but cannot print off at weekend (don't ask:!: )
Bigtone53
 
Posts: 413
Joined: 19 September 2005

Postby Bigtone53 » Mon Jul 07, 2008 10:24 am

OK, not exactly Yeasy Peasy but got the Y one out of the way.

The leading diagonal of the solution is
417652426

[later] as is the leading diagonal of all the answers, ie the same answer fits all. Surely not:?:
Bigtone53
 
Posts: 413
Joined: 19 September 2005

Postby udosuk » Mon Jul 07, 2008 11:31 am

Bigtone53 wrote:the same answer fits all. Surely not:?:

But of course! The original puzzle (depicted above) has only one unique solution, so the 4 easier versions (with various sumless cages added on) must all lead to the same unique solution.

Now that's a nice piece of logic, isn't it?:)


BTW well done on the Y. It probably takes a bit more advance techniques to solve the other versions.:idea:
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby Bigtone53 » Mon Jul 07, 2008 12:57 pm

odusuk said wrote:It probably takes a bit more advance techniques to solve the other versions.


I am sure that you are right, but having seen the final answer, I have a real problem with trying to forget it to solve in another way. I will try the others next week Great problem though:D
Bigtone53
 
Posts: 413
Joined: 19 September 2005

Postby Bigtone53 » Mon Jul 07, 2008 1:55 pm

BTW,
Before starting to think about the hints (your extra cages), I got to this through logic

42317/68--
816---7--
5974-8-6-
-3-----8-
982-5-6--
-7-8-----
2587-1-3-
769-----8
341289576


The 7/6 in line 1 makes up the 13 in some order.

I would have put this into a nice grid but do not know how to minimise it for others still working on it. Should I have got further without the use of your hints?
Bigtone53
 
Posts: 413
Joined: 19 September 2005

Postby udosuk » Tue Jul 08, 2008 1:29 am

Bigtone53 wrote:Should I have got further without the use of your hints?

Yes there is a very obvious move which I'm surprised you've missed.

Actually you've solved the bulk of the puzzle there and with that obvious move I mentioned I think you can easily solve the whole thing. What I'm curious to know is your "logic" to determine r34c8 and r9c89. For me they needed very advanced chain moves to crack.:?:
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby Bigtone53 » Tue Jul 08, 2008 8:43 am

I guess it depends on how far back I go to start

There was a stage when I had filled in all the sum squares except the 13 in r1 (67 in some order) and the 14, 9 and 11 in c89. I knew that r9c89 was 67 in some order as the 18 could only be 567, the 89 having been used.
I was also able to show that r123c1 was 458 in some order which led to r1c89 being 59 in some order which led to r34c8 being 68 and hence r9c8 being 7.

I can see that I am going to have to do it again and record what I do:(
Bigtone53
 
Posts: 413
Joined: 19 September 2005

Postby udosuk » Thu Jul 10, 2008 8:31 am

Here is another one (different puzzle, different solution), solvable with a greater variety of techniques::)

Image

Easier version

Very Easy version:D

:)
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby udosuk » Thu Jul 10, 2008 2:27 pm

Here is a brief "walkthrough" for the first puzzle (normal version). Bigtone53, please see if you can replace some of the trickier moves.

Here is the walkthrough I wrote:The cage sums must be as the following pattern:

Code: Select all
    10  13  15

  12  04  08  14

16  02  05  06  09

  19  07  01  11

    03  17  18

After basic moves:

Code: Select all
+-------------+------------------+-----------------------+
| 45   2   3  | 1     7      6   | 8      459    459     |
| 148  18  6  | 359   239    235 | 7      1234   1234    |
| 15   9   7  | 4     23     8   | 123    56     12356   |
+-------------+------------------+-----------------------+
| 168  3   45 | 689   1249   247 | 1249  #89     1245789 |
| 9    18  2  | 38    5      347 | 6      13478  1478    |
| 168  7   45 | 3689  12349  234 | 12349  1258   1234589 |
+-------------+------------------+-----------------------+
| 2    5  @89 | 7     6      1   | 349   *39     3489    |
| 7    6  @89 | 35    34     345 | 129   -1289  *28      |
| 3    4   1  | 2     8      9   | 5      67     67      |
+-------------+------------------+-----------------------+

11/2 @ r7c8=[38|92]
=> Either r7c8=9 or r8c9=8
=> r78c3 can't be [98], must be [89]

r4c8+r7c8+r8c9=[838|892|938] must have 8
=> r8c8, seeing all 3 cells, can't be 8
=> HS @ r8: r8c9=8 => r7c8=3
=> 3 @ r5,n5 locked @ r5c46

9/2 @ r5c9=[18|45|72] => r6c8 from {258}

Code: Select all
+-------------+----------------+---------------------+
| 45   2   3  | 1    7     6   | 8      459   459    |
| 148 *18  6  | 359  239   235 | 7      124   1234   |
|*15   9   7  | 4    23    8   | 123   *56    12356  |
+-------------+----------------+---------------------+
| 168  3   45 | 689  1249  247 | 1249  *89    124579 |
| 9   *18  2  | 38   5    @347 | 6      1478 -147    |
| 168  7   45 | 689  1249 @24  | 12349 -258   123459 |
+-------------+----------------+---------------------+
| 2    5   8  | 7    6     1   | 49     3     49     |
| 7    6   9  | 35   34    345 | 12     12    8      |
| 3    4   1  | 2    8     9   | 5      67    67     |
+-------------+----------------+---------------------+

r3c1+r25c2+r34c8=[18159|18168|51868|58168]
=> r5c2+r4c8=[19|18|88|18]
=> Either r5c2=1 or r4c8=8 or both
=> 9/2 @ r5c9 can't be [18], must be [45|72]
=> Either r5c9=4 or r6c8=2
=> r56c6 can't be [42]
=> r5c6 can't be 4

Code: Select all
+-------------+----------------+---------------------+
| 45   2   3  | 1    7     6   | 8      459   459    |
| 148  18  6  | 359  239   235 | 7      124   1234   |
| 15   9   7  | 4    23    8   | 123    56    12356  |
+-------------+----------------+---------------------+
| 168  3   45 | 689  1249  247 | 1249   89    124579 |
| 9    18  2  | 38   5     37  | 6      1478  47     |
| 168  7   45 | 689  1249  24  | 12349  25    123459 |
+-------------+----------------+---------------------+
| 2    5   8  | 7    6     1   | 49     3     49     |
| 7    6   9  | 35   34    345 | 12     12    8      |
| 3    4   1  | 2    8     9   | 5      67    67     |
+-------------+----------------+---------------------+

4 @ r5,n6 locked @ r5c89
HS @ c7: r7c7=4 => r7c9=9
HS @ r1: r1c8=9
=> 14/2 @ r3c8=[68]
HS @ c8: r6c8=5
=> 9/2 @ r5c9=[45]

All naked singles from here.

:idea:
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby Bigtone53 » Fri Jul 11, 2008 10:19 am

udosuk wrote:Here is another one (different puzzle, different solution), solvable with a greater variety of techniques:


Three attempts, each time reaching the same contradiction almost at the end. I am obviously making the same mistake each time but I don't see it.:(
Bigtone53
 
Posts: 413
Joined: 19 September 2005

Postby udosuk » Fri Jul 11, 2008 3:13 pm

Bigtone53 wrote:Three attempts, each time reaching the same contradiction almost at the end. I am obviously making the same mistake each time but I don't see it.:(

If you like please post a pencilmark grid so I can tell if you've gone wrong or not. Alternatively I can post the solution grid to let you check if you've eliminated a wrong candidate.
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby Bigtone53 » Fri Jul 11, 2008 5:33 pm

Let me see whether I can send you where I have got to (it will be Monday though). I do not do pencilmarks so all I can do is show you where I am and you can point out the wrong ones. I do not think that this is going to help me much in finding where I went wrong.:(

It is all to do with the 10 cage in the top left
Bigtone53
 
Posts: 413
Joined: 19 September 2005

Next

Return to Sudoku variants

cron