1to91to91to9

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1to91to91to9

Postby m_b_metcalf » Sat Sep 12, 2020 8:15 am

Following on from the recent postings with the digits of pi, here's one (not minimal but not trivial) with the digits 1 to 9, thrice, in order:
Code: Select all
 . . . . 1 . 2 3 .
 . . . 4 . . 5 . 6
 . . 7 8 . . . 9 1
 . 2 . . 3 4 . . .
 . 5 . . . . 6 . .
 7 . . . . 8 . . .
 9 1 2 3 . . . . 4
 5 6 . . . 7 8 . .
 . . . . . . . . 9


Regards,

Mike
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Re: 1to91to91to9

Postby mith » Sat Sep 12, 2020 4:31 pm

Nice. :) I retooled my pi script to check for symmetrical versions of this, here's the first non-trivial one (easier than Mike's):

Code: Select all
+-------+-------+-------+
| 1 2 3 | 4 . 5 | 6 7 . |
| 8 . . | . . . | . . . |
| . 9 . | 1 . . | . . . |
+-------+-------+-------+
| . . . | 2 . . | 3 4 . |
| . . . | . 5 . | . . . |
| . 6 7 | . . 8 | . . . |
+-------+-------+-------+
| . . . | . . 9 | . 1 . |
| . . . | . . . | . . 2 |
| . 3 4 | 5 . 6 | 7 8 9 |
+-------+-------+-------+
1234.567.8.........9.1........2..34.....5.....67..8........9.1.........2.345.6789


There are plenty of these, and some have each set constrained to a different band; I'll look for some non-trivial ones there to post eventually.
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Re: 1to91to91to9

Postby Cenoman » Sat Sep 12, 2020 10:38 pm

Mike's puzzle. A solution with AIC's only:
Code: Select all
 +-----------------------+------------------------+-----------------------+
 |  46     489   5       |  67-9    1      69     |  2     3       78     |
 |  12     89    19      |  4       279    3      |  5     78      6      |
 |  26     3     7       |  8       256    256    |  4     9       1      |
 +-----------------------+------------------------+-----------------------+
 |  18     2     1689    |  1567-9  3      4      |  19    178     578    |
 |  348-1  5     13489   |  1279    279    129    |  6     1248-7  28-37  |
 |  7      49    13469   |  12569   2569   8      |  139   124     235    |
 +-----------------------+------------------------+-----------------------+
 |  9      1     2       |  3       8      56     |  7     56      4      |
 |  5      6     34      |  19      49     7      |  8     12      23     |
 |  348    7     348     |  1256    2456   1256   |  13    56      9      |
 +-----------------------+------------------------+-----------------------+

1. (3)r6c79 = r6c3 - r8c3 = r8c9 => -3 r5c9
2. (9=1)r8c4 - r9c6 = (1-9)r5c6 = (9)r1c6 => -9 r1c4
3. (9=1)r8c4 - r8c8 = r9c7 - (1=9)r4c7 => -9 r4c4
4. (4)r5c8 = r6c8 - r6c2 = (4-8)r1c2 = (8-*7)r1c9 = r1c4 - r2c5 = r5c5 => -7 r5c8, r5c9*
5. (3)r5c1 = r9c1 - (3=1)r9c7 - r9c6 = (1)r5c6 => -1 r5c1
Code: Select all
 +----------------------+------------------------+---------------------+
 |  46    489   5       | a67      1      69     |  2     3     b78    |
 | B12   C89   C19      |  4       279    3      |  5    C78     6     |
 |  26    3     7       |  8       256    256    |  4     9      1     |
 +----------------------+------------------------+---------------------+
 | A18    2     1689    | d5-16    3      4      |  9-1   178   c578   |
 |  348   5     13489   |  1279    279    129    |  6     1248   28    |
 |  7     49    1469    |  12569   2569   8      |  139   124    235   |
 +----------------------+------------------------+---------------------+
 |  9     1     2       |  3       8      56     |  7     56     4     |
 |  5     6     34      |  19      49     7      |  8     12     23    |
 |  348   7     348     |  1256    2456   1256   |  13    56     9     |
 +----------------------+------------------------+---------------------+

6. (6=7)r1c4 - r1c9 = (7-5)r4c9 = (5)r4c4 => -6 r4c4
7. (1)r4c1 = r2c1 - (1=987)r2c238 - (7=81)r4c18 => -1 r4c47; ste
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Re: 1to91to91to9

Postby m_b_metcalf » Sun Sep 13, 2020 8:05 am

mith wrote:There are plenty of these, and some have each set constrained to a different band;

As here:
Code: Select all
 . 1 . . . 2 . 3 .
 4 . 5 . 6 7 . . .
 . . 8 . 9 . . . .
 1 . 2 . . . 3 . .
 . . . . . . . . 4
 . 5 6 . . . 7 8 9
 . . . . 1 . . . 2
 . . . . 3 4 5 6 .
 7 . . . 8 . . 9 .        Mike 2


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