Pi

Everything about Sudoku that doesn't fit in one of the other sections

Pi

Postby m_b_metcalf » Fri Sep 11, 2020 2:58 pm

mith, elsewhere, wrote:27 digits appears to be the max for a symmetrical pi puzzle; you can get 32 - all the digits before the first 0 - without symmetry, though I haven't looked very far to see if there's actually an interesting puzzle there.

mith, do you have an example of a valid puzzle with all the first 32 non-zero clues? My first attempt was
Code: Select all
 . . . 3 1 . 4 . .
 1 . . . . . . 5 .
 9 2 6 . . 5 3 . .
 5 . 8 . . . 9 . .
 . . 7 9 . 3 . 2 .
 . . 3 . 8 4 6 . .
 . . . 2 6 . . 4 3
 . . . . 3 8 . . .
 3 . 2 . 7 9 5 . .  No. of givens =  32

found 9 solution(s)

Adding 6r1c6 yields a valid puzzle.

Thanks,

Mike
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Re: Pi

Postby mith » Fri Sep 11, 2020 4:07 pm

I misspoke; there was a bug in my script causing it to return as soon as it found a valid puzzle, even if it didn't have all the digits. I'll have to fix it at some point and run it again.
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Re: Pi

Postby m_b_metcalf » Fri Sep 11, 2020 4:31 pm

mith wrote:I misspoke; there was a bug in my script causing it to return as soon as it found a valid puzzle, even if it didn't have all the digits. I'll have to fix it at some point and run it again.

Thanks. I'm getting closer:
Code: Select all
 . . 3 . 1 . . 4 .
 1 . . . . . . 5 9
 . 2 6 . 5 . . 3 .
 . 5 . 8 . 9 . . 7
 . . 9 3 . 2 . . .
 3 8 . . 4 . . 6 2
 . . . 6 . . 4 . 3
 . . . . . 3 . . 8
 . 3 2 . . 7 . 9 5
No. of givens =  32, found 3 solution(s)
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Re: Pi

Postby mith » Fri Sep 11, 2020 5:31 pm

I quite like that one. The decimal point between the 3 and the 1 gives the three unique solutions if assigned.
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Re: Pi

Postby m_b_metcalf » Fri Sep 11, 2020 5:36 pm

Bingo!

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

No. of givens =  32

singles found 1 solution
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Re: Pi

Postby mith » Fri Sep 11, 2020 5:53 pm

Very nice!
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Re: Pi

Postby Mathimagics » Fri Sep 11, 2020 6:18 pm

I like π, as you can imagine.

You might be able to extend the number of clues beyond 32 by simply treating that pesky 0 in position 33 as a normal non-given, but displayed as 0, not a dot, in the puzzle string.

So, can you do 34 digits (33 clues)? 35?

36 could be a real problem, with the repeating digit pair 35 = 36 = "8", and you are probably in the last row by that stage ...
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Re: Pi

Postby mith » Fri Sep 11, 2020 6:33 pm

You actually can't go any farther (other than adding the 0 at the end, if there is room).

Digit 2 (1) forces Digit 4 (1) to row 2.
Digit 5 (5) forces Digit 9 (5) to row 3, which forces Digit 11 (5) to row 4.
Digit 13 (9) forces Digit 15 (9) to row 5.
Digit 16 (3) forces Digit 18 (3) to row 6.
Digit 21 (6) forces Digit 23 (6) to row 7.
Digit 25 (3) forces Digit 26 (3) to row 8, which forces Digit 28 (3) to row 9.
Digit 29 (2) rules out placing Digit 34 (2).
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Re: Pi

Postby Mathimagics » Fri Sep 11, 2020 11:50 pm

Nicely put! 32 it is ...
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Re: Pi

Postby m_b_metcalf » Sat Sep 12, 2020 6:47 am

Mathimagics wrote:I like π, as you can imagine.

And e as well, I assume:
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  31 digits of e (including 2 zeros)

I'm now going to fall into a rabbit hole and work on i. ;)

Regards,

Mike
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Re: Pi

Postby Mathimagics » Sat Sep 12, 2020 9:13 am

i before e, except after π ... so they say 8-)

That's nice, Mike!

Meanwhile, I have searched through the first billion digits of π and can find no 81-digit sequence that forms a valid puzzle. :(

I looked also at e, ϕ, and even Euler's constant (thought I just might get lucky there!) ... no cigar! :cry:

Probability theory is a hard task master ... monkeys, typewriters, Shakespeare, etc ...

Would anyone care to look at the 22 trillion digits of π that are available?
Last edited by Mathimagics on Sat Sep 12, 2020 9:26 am, edited 1 time in total.
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Re: Pi

Postby m_b_metcalf » Sat Sep 12, 2020 9:26 am

Mathimagics wrote:Sad news: I have searched through the first billion digits of π and can find no 81-digit sequence that forms a valid puzzle.

Interesting. Was it even close? What was the maximum number of complete rows that you achieved?
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Re: Pi

Postby Mathimagics » Sat Sep 12, 2020 9:30 am

That information is not available, sorry! :?

I just looped over the data, advancing the grid pointer by one at each step, and simply called my fsss2 solver. Got zero (invalid) every time ...
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Re: Pi

Postby JPF » Sat Sep 12, 2020 7:33 pm

m_b_metcalf wrote:Bingo!

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

No. of givens =  32

singles found 1 solution

Excellent!
This reminds me of a good old RW riddle here

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Re: Pi

Postby m_b_metcalf » Mon Sep 14, 2020 11:56 am

mith wrote:You actually can't go any farther (other than adding the 0 at the end, if there is room).

Still working on that, but the best so far is
Code: Select all
 . . 3 1 . . . 4 .
 1 5 . . . . 9 . .
 2 . 6 5 . . . . 3
 5 . 8 . . . . 9 7
 . . 9 3 . . 2 . .
 3 . . . 8 4 . 6 .
 . . . 2 6 . 4 3 .
 . . . . 3 8 . . .
 . 3 2 7 9 . . 5 0

No. of givens =  32, plus a zero
found 4 solution(s)
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