The New Sudoku Players' Forum

[Hajime]

e=2.71828 18284 59045 23536 02874 71352 66249 77572 47093 69995...
π=3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510...

e has a 0 much earlier in the decimal representation as π has. But a 0 can be an empty cell in a Sudoku.
Like the constant π, e is irrational (that is, it cannot be represented as a ratio of integers) and transcendental (that is, it is not a root of any non-zero polynomial with rational coefficients)
π is a irrational number, also e is irrational, e =
but with more association with Sudoku. Watch:
Source Wikipedia
It has n! enumerated, like Sudoku possibilities has...

I see various π puzzles, but no e puzzles.... and after a couple of days, I still can't produce one. Can you?

[mith]

There's this one: pi-t38253.html#p294938

I haven't messed with e much myself, but I have been making some small sqrt(2) puzzles. For example:

Code: Select all

+-------+-------+
| 1 . . | . . . |
| . 4 . | . . . |
+-------+-------+
| . . 1 | . . . |
| . 2 . | 4 . . |
+-------+-------+
| 6 . . | . 2 . |
| . 5 . | 3 . 1 |
+-------+-------+

[JPF]

Code: Select all

..12345..
.5.....3.
.4.....6.
.6.....7.
.859714..
.2.......
.3.......
..9......
...4861..


JPF

[Hajime]

Code: Select all

..12345..
.5.....3.
.4.....6.
.6.....7.
.859714..
.2.......
.3.......
..9......
...4861..


JPF

[denis_berthier]

Code: Select all

..12345..
.5.....3.
.4.....6.
.6.....7.
.859714..
.2.......
.3.......
..9......
...4861..


JPF

It has a solution with Singles. I tried to generate harder ones, but this pattern has comparatively few minimal puzzles. Here is the hardest I found after two hours of computation with gsf's program:

Code: Select all

..83476...2.....1..5.....9..8.....4..641927...9........7.........1.........2768..
SER = 7.1

[JPF]

I should have proposed this one:

Code: Select all

..12345..
.5.....6.
.7.....1.
.8.....5.
.325764..
.1.......
.4.......
..7......
...6173..


SER = 8.3 (> e^2)

JPF

[Leren]

Code: Select all

*----------------------------------------------------------*
| 8-6     69  1      | 2     3      4    | 5      79 789   |
| 2348    5   3489   | 7     89     1    | 289    6  34    |
| 2348    7   3489   | 89    6      5    | 289    1  34    |
|--------------------+-------------------+-----------------|
| 467     8   46     | 1     249    3    | 679    5  2679  |
| 9       3   2      | 5     7      6    | 4      8  1     |
| 4567    1   456    | 489   2489   289  | 679    3  2679  |
|------ -------------+-------------------+-----------------|
| 13568   4   35689  | 389   2589   289  | 16789 279 56789 |
| 13568   69  7      | 3489  24589  289  | 1689  29 *5689  |
| 58      2  589     | 6     1      7    | 3      4  589   |
*----------------------------------------------------------*

Kraken Cell r8c9:

6 r1c1 - (6=9) r1c2 - r1c8 = r78c8 - r9c9                     = (9-5) r9c3

6 r1c1 - 8r1c1 = 8r1c9                        - 8 r9c9

6 r1c1 - (6=9) r1c2 - r1c8 = r78c8 - r9c9 = (9-8) r9c3 *=  8 r9c1 - 5 r9c1 *= 5 r9c9 - 5 r8c9

6 r1c1 - 6 r1c2 = 6 r8c2                                                             - 6 r8c9;

6 r1c1 - 8 r1c1 = 8 r1c9                                                             - 8 r8c9;

6 r1c1 - (6=9) r1c2 - 9 r1c8 = 9 r78c8                                               - 9 r8c9; => - 6 r1c1; stte

Messy, but I think it works. Ye- eeeeeeeeeeeeee Hah !

Leren

[Cenoman]

Code: Select all

 +-----------------------+-----------------------+------------------------+
 |  68    Ab69   1       |  2      3       4     |  5     Ad79   A789     |
 |  2348    5    3489    |  7      89      1     |  289     6     34      |
 |  2348    7    3489    |  89     6       5     |  289     1     34      |
 +-----------------------+-----------------------+------------------------+
 |  467     8    46      |  1      249     3     |  679     5     2679    |
 |  9       3    2       |  5      7       6     |  4       8     1       |
 |  4567    1    456     |  489    2489    289   |  679     3     2679    |
 +-----------------------+-----------------------+------------------------+
 |  13568   4    35689   |  389    2589    289   |  16789  d279   56789   |
 |  13568 Ba69x  7       |  3489   24589  B289   |  168-9 Bd29   56-89w   |
 | B'58     2   B'589y   |  6      1       7     |  3       4     9-85z   |
 +-----------------------+-----------------------+------------------------+

1. (9)r8c2 = r1c2 - r1c8 = r78c8 => -9 r8c79
2. (8=796)r1c289 - (6=298)r8c268 => -8 r8c9
3. (8=796)r1c289 - (6=598)b7p579 => -8 r9c9
4. (5=6)r8c9-(6=9)r8c2-r9c3=(9)r9c9 => -5 r9c9; ste

[Hajime]

I foresee a new topic with 2*26 (lower and upper case) and 10 digit puzzles

[m_b_metcalf]

mith remined me that I'd already produced an e puzzle, but then I couldn't remember how I'd done it. In reminding myself, I produced a slightly better one, with an extra digit:

Code: Select all

 2 . . 7 1 8 . . .
 . . . 2 . . 8 . 1
 . 8 . . . . 2 . .
 . . 8 4 . . 5 . 9
 0 . 4 5 2 . . . 3
 5 . . . 3 . 6 0 .
 . . 2 . 8 7 . . 4
 . 7 1 . . 3 . 5 2
 . . 6 . . . . . .

No. of givens =  32, including 2 zeros

[999_Springs]

I foresee a new topic with 2*26 (lower and upper case) and 10 digit puzzles

m_b_metcalf already did it in 2007

[Cenoman]

One step solution to JPF's puzzle:

Code: Select all

 +-----------------------+-----------------------+--------------------------+
 | d68     e69   1       |  2      3       4     |  5       79     d789     |
 |  2348    5    3489    |  7      89      1     |  289     6       34      |
 |  2348    7    3489    |  89     6       5     |  289     1       34      |
 +-----------------------+-----------------------+--------------------------+
 |  467     8    46      |  1      249     3     |  679     5       2679    |
 |  9       3    2       |  5      7       6     |  4       8       1       |
 |  4567    1    456     |  489    2489    289   |  679     3       2679    |
 +-----------------------+-----------------------+--------------------------+
 |  13568   4    35689   |  389    2589    289   |  16789   27-9    56789   |
 |  13568  f69   7       |  3489   24589   289   |  1689    2-9  cba5689    |
 |  58      2   g589     |  6      1       7     |  3       4    hca589     |
 +-----------------------+-----------------------+--------------------------+

Almost-almost hidden pair (kraken AALS):
(59)r89c9 = [(6)r8c9*=*(8)r89c9 - (86)r1c19 = r1c2] - (6=9)r8c2 - r9c3 = (9)r9c9 => -9 r78c8; ste

TM 6x6

Hidden Text: Show

Code: Select all

9r9c9 9r9c3
      9r8c2 6r8c2
            6r1c2 6r1c1
                  8r1c1 8r1c9
9r8c9       6r8c9       8r8c9 5r8c9
9r9c9                   8r9c9 5r9c9
----------------
=> -9 r78c8; ste

[m_b_metcalf]

I haven't messed with e much myself, but I have been making some small sqrt(2) puzzles. For example:
...

sqrt(2) = 1.4142135623730950488016887242096[9807856967187537694807317667973799...] is a bit tricky. My best yet is:

Code: Select all

 . . . 1 . . . . 4
 . . 1 . 4 . 2 . .
 . . . . . . . 1 3
 . 5 6 2 . 3 . 7 .
 3 0 9 5 0 4 8 . .
 8 0 . . . 1 . . .
 6 . . . . 8 . . .
 . . 8 7 . 2 4 . .
 . . 2 0 . 9 . 6 .

No. of givens =  28 + 4 zeros

brute found 1 solution(s)

Regards,

Mike

[mith]

Nice 32 digit e!

Yeah, for root 2 (without 0s) I've done the regular 6x6, an irregular 7x7, and an irregular 8x8 with one extra variant clue (a sandwich 14; eventually I'll revisit this to try to make it work as a classic irregular), all with this right triangle shape. Presumably 4x4 and 5x5 are doable too.

Here are a couple more:

Code: Select all

+-------+-------+-------+
| 3 . . | 2 1 . | . . . |
| . . . | 7 . . | 4 1 . |
| . . 1 | . . . | 8 . . |
+-------+-------+-------+
| . 5 . | . . . | . . 2 |
| . . 9 | 8 . 2 | 1 . . |
| 6 . . | . . . | . 8 . |
+-------+-------+-------+
| . . 5 | . . . | 2 . . |
| . 3 8 | . . 5 | . . . |
| . . . | . 4 8 | . . 5 |
+-------+-------+-------+
3..21.......7..41...1...8...5......2..98.21..6......8...5...2...38..5.......48..5 (alternating π & e)

I think 25 is the max for a rotationally symmetric grid with this digit order; there are a lot of 25s (I stopped it running after a while with a high SER of 7.8), the above is 24 so that both numbers are equally represented (I only found 12 of these grids with 12 digits apiece!).

Code: Select all

+-------+-------+-------+
| 1 3 9 | 2 7 . | . . . |
| . . . | . . . | 8 1 . |
| . 2 . | . . . | . . . |
+-------+-------+-------+
| 4 . . | . . 3 | 7 2 9 |
| . . . | . . . | . . . |
| 2 1 8 | 7 . . | . . 6 |
+-------+-------+-------+
| . . . | . . . | . 5 . |
| . 6 1 | . . . | . . . |
| . . . | . 1 9 | 6 8 3 |
+-------+-------+-------+
13927..........81..2.......4....3729.........2187....6.......5..61..........19683 (powers of 3)

[Leren]

How about square root of 3 = 1.73205080756887729352744634150587236694280525381038062805580697945193301690880003708114618675724857567562614141540670302996994509499895247881165551209437364852809323190230558206797482010108467492326501531234326690332288665067225466892183 etc etc > infinity

Being a former electrical engineer, that's the ratio of phase quantities to line to line quantities, so it's at least useful. Any Root 3 puzzlers out there ? Leren