The New Sudoku Players' Forum

by **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 (94.32 KiB) Viewed 1445 times

by **Mathimagics** » Wed Apr 06, 2016 3:09 pm

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

: Kakuro Xword Clues (Revised 14/4/2016); KakuroXword_Guide.jpg (138.44 KiB) Viewed 1424 times

Solution to the example above:

Hidden Text: Show

by **Mathimagics** » Thu Apr 07, 2016 4:02 pm

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

: KT0909_T001.jpg (67.68 KiB) Viewed 1438 times

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

by **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.

Bill Smythe

by **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

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