Kakuro Xword

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Kakuro Xword

Postby Mathimagics » Wed Apr 06, 2016 3:06 pm

I've created a number crossword puzzle that is based on Kakuro, but with a variety of clue types - Kakuro sums, Skyscraper, plus various other clues that identify number properties.

Here is an example that demonstrates the basic idea:

KX1010_P002.jpg
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Last edited by Mathimagics on Wed Apr 06, 2016 3:35 pm, edited 1 time in total.
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Kakuro Xword - Clue guide

Postby Mathimagics » Wed Apr 06, 2016 3:09 pm

Here is a guide to the clue format (revised 14 April 2016):

KakuroXword_Guide.jpg
Kakuro Xword Clues (Revised 14/4/2016)
KakuroXword_Guide.jpg (138.44 KiB) Viewed 136 times


Solution to the example above:
Hidden Text: Show
3254x31xx
86352491x
13x257861
45271x643
x9714823x
241x86351
374291x79
x16539427
xx31x7193
Last edited by Mathimagics on Wed Apr 13, 2016 2:24 pm, edited 1 time in total.
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Kakuro Xword - Sample (misc clues)

Postby Mathimagics » Thu Apr 07, 2016 4:02 pm

Here's an example with a mixture of clue types:

KT0909_T001.jpg
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These Kakuro word lists might be useful for this puzzle:
Code: Select all
Primes
  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73  79  83
  89  97

 127 137 139 149 157 163 167 173 179 193 197 239 241 251 257 263 269 271
 281 283 293 317 347 349 359 367 379 389 397 419 421 431 439 457 461 463
 467 479 487 491 521 523 541 547 563 569 571 587 593 613 617 619 631 641
 643 647 653 659 673 683 691 719 739 743 751 761 769 821 823 827 829 839
 853 857 859 863 937 941 947 953 967 971 983

EPrimes
  12  14  24  26  28  34  38  46  48  52  56  58  62  68  74  76  82  86
  92  94  96

 124 134 136 142 146 148 152 158 164 172 176 178 184 192 194 214 218 236
 248 254 268 274 278 284 296 298 314 316 326 328 346 352 356 358 362 368
 376 382 384 386 394 398 412 416 428 436 452 458 472 478 482 496 514 524
 526 536 538 542 548 562 568 584 586 592 596 614 628 632 634 652 674 692
 694 698 712 716 718 724 734 736 746 752 758 764 768 794 796 824 832 842
 856 862 872 892 896 914 916 926 928 932 934 956 958 964 974 976 982


Solution:
Hidden Text: Show
154x521
236x412
3974256
47568xx
5837624
6428375
xx15732
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Re: Kakuro Xword

Postby Smythe Dakota » Fri Apr 08, 2016 5:12 am

When I was in college (decades ago!) I created a cross-number puzzle that was essentially a crossword puzzle with digits in place of letters. The clues, though, were written in English. One clue I had (for a six-digit number) was "a million less than the cube of a factorial".

There was no repeating-digits prohibition, only a prohibition on any "word" starting with the digit 0.

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Re: Kakuro Xword

Postby Mathimagics » Fri Apr 08, 2016 7:21 am

Yes, I've seen those puzzles, and have actually done some, and while KXW has a similar presentation, the resemblance is superficial, ie. the crossword layout.

KXW is an egalitarian puzzle, it gives a home to all of those millions of unwanted Kakuro grids - the ones whose sums are not unique. All grids are potential puzzles! 8-)

I've been applying the DIY test to a KXW puzzle on a 14x14 grid with minimal (reduced) clues, and it passes, IMHO. It's challenging, it's different, and it's fun!

And educational, perhaps ... for example, in producing word lists for properties P, EP, SQ etc, I discovered that the properties "SQ, D5" can only apply to two particular values 25, and 625. I was curious as to why this is so.

Clearly the number must an odd square and a multiple of 25, and it becomes clear when you arrange these numbers, k^2 x 25 (k = 1, 3, 5...) in columns of 5:

Code: Select all
   25     225     625    1225    2025
 3025    4225    5625    7225    9025
11025   13225   15625   18225   21025
24025   27225   30625   34225   38025
42025   46225   50625   55225   60025
65025   70225   75625   81225   87025
.....   .....   .....   .....   .....

As you can see, column 1 (k mod 5 = 1) has a zero in every case apart from the first entry, column 5 has a zero in every entry, columns 2 and 4 all end in 225 (not a K-word), which leaves column 3. This column, apart from the first entry, has a zero or a 5 in the thousands position ...

All other SQ K-words end in 1,4,6 or 9 with roughly equal distribution. They are quite rare, so I can give the full list:
Hidden Text: Show
16 25 36 49 64 81

169 196 256 289 324 361
529 576 625 729 784 841
961

1296 1369 1764 1849 1936 2916
3249 3481 3721 4356 4761 5184
5329 5476 6241 6724 7396 7569
7921 8649 9216

12769 13456 13689 13924 15376 15876
16384 17689 17956 18496 18769 23716
28561 29584 31684 32761 34596 35721
36481 37249 38416 43681 45369 45796
47961 51984 53824 54289 71289 71824
72361 73984 74529 78961 79524 81796
82369 83521 85264 92416 95481 96721

132496 134689 139876 195364 214369 237169
279841 293764 321489 327184 329476 346921
349281 351649 379456 381924 385641 391876
395641 436921 458329 524176 537289 543169
582169 651249 687241 729316 751689 758641
781456 872356

1238769 1247689 1354896 1382976 1763584 2374681
2537649 3297856 3481956 3594816 3857296 4519876
5184729 5391684 5673924 5827396 5948721 6385729
6395841 6538249 6853924 7139584 7214596 7349521
7436529 7458361 8213956 8317456 8473921 8567329
9247681 9253764 9357481 9572836 9678321 9872164

13498276 13527684 13942756 21473956 21743569 23174596
24137569 34857216 36517849 38142976 41783296 41938576
45387169 45738169 46389721 52374169 54213769 65318724
73256481 74356129 81432576

139854276 152843769 157326849 215384976 245893761 254817369
326597184 361874529 375468129 382945761 385297641 412739856
523814769 529874361 537219684 549386721 587432169 589324176
597362481 615387249 627953481 653927184 672935481 697435281
714653289 735982641 743816529 842973156 847159236 923187456
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