## minimum number of clues 16x16 and higher

For fans of Killer Sudoku, Samurai Sudoku and other variants

### minimum number of clues 16x16 and higher

What is the minimum number of clues required for a 16x16 sudoku?

More realistically, what is the current record?

Using a 4x4 sudoku which requires 4 clues:
1234
3412
2143
4321
we can make a grid

1234567890etabcd
et90cdab34127856
dcbate0987654321
90etabcd12345678
34127856et90cdab
87654321dcbate09
56781234abcd90et
cdabet9078563412
te09dcba43218765
abcd90et56781234
78563412cdabet90
43218765te09dcba

This is partitioned into 16 of the above 4x4 sudokus.

Any puzzle from this grid will require at least 64 clues since these 4x4 sudokus require 4 clues.

[edit: rubbish deleted]

Then, what is the current record for 25x25 sudoku, and higher?
Last edited by Moschopulus on Fri Aug 12, 2005 11:47 am, edited 1 time in total.
Moschopulus

Posts: 256
Joined: 16 July 2005

you proved that 64 is required at least for any 16*16
sudoku whose unique solution is the one you posted.

the minimum number of clues could be 70-80, I guess.

I tried to remove clues from larger 16*16 sudokus, as I've learned
it with 9*9 ones. I hardly can get below 90.
Found one with 86, some with 89, lots with 90.
Last edited by dukuso on Fri Aug 12, 2005 11:58 am, edited 1 time in total.
dukuso

Posts: 479
Joined: 25 June 2005

Sorry. I was claiming some rubbish, but not any more. Thanks.

I don't suppose one of those sets of 64 clues works.

Checking this would be like the computation you did with the 1296 cases.
Moschopulus

Posts: 256
Joined: 16 July 2005

What do you think of this 16x16 sudoku? The paper said it was a 1 star.
I say it is impossible it is 1 star but it has to be a 5 star (hardest).
Here it is. What do you think? 1 or 5 stars?

*5** 6**E *F*C *0**
B**0 24** *1*3 5*E*
*E** *D*1 5*** ****
**9F **C* **2* *418

*02* F3E* *97* **4*
6C4D **** **1* E2**
***5 **** B8** 7DF*
F*** **D* 3*A* ***9

0*** *E*C *B** ***F
*2DC **73 **** 8***
**F3 *8** **** 27BA
*8** *2A* *3FD *19*

DAB* *C** *E** 19**
**** ***2 8*C* **D*
*9*E 8*5* **BA F**6
**C* E*B* 7**9 **2*

After 4 hours of working on it, I could only determine 19 of the missing values:

*5** 6**E *F*C *0**
B**0 24** *1*3 5*E*
CE** *D*1 5*** ****
**9F **C* **2* *418

*02* F3E* D976 **4*
6C4D **** **1* E2*3
93*5 C*2* B8** 7DF*
FBE7 **D* 3CA2 ***9

0**9 *E*C *B** D*3F
*2DC *F73 **** 8***
**F3 *8** **** 27BA
*8** *2A* *3FD *19*

DAB* *C** *E** 19**
**** ***2 8*C* **D*
*9*E 8*5* **BA F3C6
**C* E*B* 7**9 **2*
monstersudoku

Posts: 4
Joined: 10 August 2005

### Re: minimum number of clues 16x16 and higher

25816B3E4F9CA07D
B6702498A1D35FEC

802AF3E5D976BC41
6C4D798BF015E2A3
9315C62AB84E7DF0
FBE741D03CA26859

04A91E6C2B87D53F
52DCBF739AE18604
E1F3D809C56427BA
786B52A403FDC19E

DAB23C4F6E501987
37569A1284CF0EDB
490E875D12BAF3C6
1FC8E0B67D394A25

after 28 ms. The puzzle is very easy since it uses only hidden and naked singles: Her the "raw" output, numbers 0..F are translated to 1..16:

hidden single in block: r3c1 = 13
hidden single in block: r7c1 = 10
hidden single in block: r7c7 = 3
hidden single in block: r5c9 = 14
hidden single in block: r9c4 = 10
hidden single in block: r12c4 = 12
hidden single in block: r10c6 = 16
hidden single in block: r9c12 = 8
hidden single in block: r9c11 = 9
hidden single in block: r9c13 = 14
hidden single in block: r3c12 = 9
hidden single in block: r4c12 = 12
hidden single in block: r4c9 = 15
hidden single in block: r8c2 = 12
hidden single in block: r8c10 = 13
hidden single in block: r10c5 = 12
hidden single in block: r9c9 = 3
hidden single in block: r1c6 = 12
hidden single in block: r7c5 = 13
hidden single in block: r8c12 = 3
hidden single in block: r15c10 = 3
hidden single in block: r13c4 = 3
hidden single in block: r1c1 = 3
hidden single in block: r3c16 = 3
hidden single in row: r8c3 = 15
hidden single in row: r9c3 = 11
hidden single in row: r11c9 = 13
hidden single in row: r13c15 = 9
hidden single in row: r15c8 = 14
hidden single in block: r8c4 = 8
hidden single in block: r11c5 = 14
hidden single in column: r15c15 = 13
Naked single: r15c14 = 4
hidden single in block: r9c15 = 4
hidden single in row: r6c16 = 4
hidden single in row: r6c8 = 12
hidden single in row: r6c7 = 9
hidden single in row: r8c14 = 9
hidden single in block: r2c8 = 9
hidden single in column: r1c3 = 9
hidden single in column: r11c8 = 10
hidden single in block: r1c4 = 2
hidden single in block: r3c4 = 5
hidden single in block: r4c1 = 11
hidden single in block: r3c5 = 11
hidden single in block: r5c4 = 11
hidden single in block: r6c15 = 11
hidden single in block: r5c1 = 9
hidden single in block: r16c4 = 9
hidden single in row: r5c16 = 2
hidden single in column: r14c4 = 7
hidden single in column: r10c10 = 11
hidden single in column: r14c16 = 12
hidden single in block: r13c16 = 8
hidden single in block: r14c14 = 15
hidden single in row: r1c15 = 8
hidden single in column: r4c8 = 8
hidden single in column: r3c10 = 8
Naked single: r1c16 = 14
Naked single: r2c16 = 13
Naked single: r3c15 = 7
Naked single: r4c13 = 4
Naked single: r7c16 = 1
Naked single: r8c13 = 7
Naked single: r8c15 = 6
Naked single: r10c15 = 1
hidden single in block: r3c3 = 4
hidden single in block: r1c7 = 4
hidden single in block: r7c2 = 4
hidden single in block: r12c13 = 13
hidden single in block: r7c3 = 2
hidden single in block: r5c14 = 13
hidden single in block: r5c13 = 12
hidden single in block: r3c14 = 12
hidden single in block: r2c14 = 16
hidden single in block: r3c7 = 16
hidden single in block: r1c13 = 11
hidden single in block: r16c14 = 11
hidden single in block: r2c7 = 10
hidden single in block: r2c9 = 11
hidden single in block: r3c13 = 10
hidden single in block: r14c6 = 11
hidden single in block: r16c16 = 6
hidden single in block: r7c8 = 11
hidden single in block: r14c5 = 10
hidden single in block: r6c6 = 10
hidden single in block: r13c5 = 4
hidden single in block: r15c6 = 8
hidden single in block: r16c11 = 4
hidden single in block: r16c10 = 14
hidden single in block: r2c11 = 14
hidden single in block: r6c5 = 8
hidden single in block: r14c1 = 4
hidden single in block: r14c3 = 6
hidden single in block: r14c2 = 8
hidden single in block: r16c2 = 16
hidden single in block: r13c8 = 16
hidden single in block: r14c12 = 16
hidden single in block: r2c3 = 8
hidden single in block: r4c2 = 14
hidden single in block: r4c10 = 7
hidden single in block: r5c8 = 6
hidden single in block: r7c6 = 7
hidden single in block: r5c12 = 7
hidden single in block: r6c9 = 16
hidden single in block: r12c1 = 8
hidden single in block: r15c3 = 1
hidden single in block: r15c9 = 2
hidden single in block: r2c2 = 7
hidden single in block: r3c11 = 1
hidden single in block: r12c3 = 7
hidden single in block: r16c1 = 2
hidden single in block: r15c1 = 5
hidden single in block: r14c7 = 2
hidden single in block: r9c5 = 2
hidden single in block: r12c5 = 6
hidden single in block: r4c6 = 6
hidden single in block: r8c6 = 2
hidden single in block: r11c2 = 2
hidden single in block: r9c2 = 5
hidden single in block: r10c12 = 2
hidden single in block: r4c5 = 1
hidden single in block: r8c8 = 1
hidden single in block: r8c5 = 5
hidden single in block: r11c7 = 1
hidden single in block: r12c8 = 5
hidden single in block: r9c7 = 7
hidden single in block: r12c9 = 1
hidden single in block: r10c16 = 5
hidden single in block: r10c14 = 7
hidden single in block: r12c16 = 15
hidden single in block: r16c6 = 1
hidden single in block: r13c7 = 5
hidden single in block: r16c8 = 7
hidden single in block: r14c10 = 5
hidden single in block: r14c13 = 1
hidden single in block: r16c13 = 5
hidden single in block: r11c11 = 7
hidden single in block: r9c14 = 6
hidden single in block: r13c12 = 1
hidden single in block: r13c11 = 6
hidden single in block: r13c9 = 7
hidden single in block: r6c10 = 1
hidden single in block: r6c12 = 6
hidden single in block: r11c12 = 5
hidden single in block: r11c10 = 6
hidden single in block: r10c11 = 15
hidden single in block: r7c11 = 5
hidden single in block: r7c12 = 15
hidden single in block: r10c1 = 6
hidden single in block: r11c1 = 15
hidden single in block: r10c9 = 10
hidden single in block: r1c9 = 5
hidden single in block: r1c11 = 10
sudoko0815

Posts: 3
Joined: 03 July 2017

### Re: minimum number of clues 16x16 and higher

25816B3E4F9CA07D
B6702498A1D35FEC

802AF3E5D976BC41
6C4D798BF015E2A3
9315C62AB84E7DF0
FBE741D03CA26859

04A91E6C2B87D53F
52DCBF739AE18604
E1F3D809C56427BA
786B52A403FDC19E

DAB23C4F6E501987
37569A1284CF0EDB
490E875D12BAF3C6
1FC8E0B67D394A25

after 28 ms. The puzzle is very easy since it uses only hidden and naked singles: Her the "raw" output, numbers 0..F are translated to 1..16:

hidden single in block: r3c1 = 13
hidden single in block: r7c1 = 10
hidden single in block: r7c7 = 3
hidden single in block: r5c9 = 14
hidden single in block: r9c4 = 10
hidden single in block: r12c4 = 12
hidden single in block: r10c6 = 16
hidden single in block: r9c12 = 8
hidden single in block: r9c11 = 9
hidden single in block: r9c13 = 14
hidden single in block: r3c12 = 9
hidden single in block: r4c12 = 12
hidden single in block: r4c9 = 15
hidden single in block: r8c2 = 12
hidden single in block: r8c10 = 13
hidden single in block: r10c5 = 12
hidden single in block: r9c9 = 3
hidden single in block: r1c6 = 12
hidden single in block: r7c5 = 13
hidden single in block: r8c12 = 3
hidden single in block: r15c10 = 3
hidden single in block: r13c4 = 3
hidden single in block: r1c1 = 3
hidden single in block: r3c16 = 3
hidden single in row: r8c3 = 15
hidden single in row: r9c3 = 11
hidden single in row: r11c9 = 13
hidden single in row: r13c15 = 9
hidden single in row: r15c8 = 14
hidden single in block: r8c4 = 8
hidden single in block: r11c5 = 14
hidden single in column: r15c15 = 13
Naked single: r15c14 = 4
hidden single in block: r9c15 = 4
hidden single in row: r6c16 = 4
hidden single in row: r6c8 = 12
hidden single in row: r6c7 = 9
hidden single in row: r8c14 = 9
hidden single in block: r2c8 = 9
hidden single in column: r1c3 = 9
hidden single in column: r11c8 = 10
hidden single in block: r1c4 = 2
hidden single in block: r3c4 = 5
hidden single in block: r4c1 = 11
hidden single in block: r3c5 = 11
hidden single in block: r5c4 = 11
hidden single in block: r6c15 = 11
hidden single in block: r5c1 = 9
hidden single in block: r16c4 = 9
hidden single in row: r5c16 = 2
hidden single in column: r14c4 = 7
hidden single in column: r10c10 = 11
hidden single in column: r14c16 = 12
hidden single in block: r13c16 = 8
hidden single in block: r14c14 = 15
hidden single in row: r1c15 = 8
hidden single in column: r4c8 = 8
hidden single in column: r3c10 = 8
Naked single: r1c16 = 14
Naked single: r2c16 = 13
Naked single: r3c15 = 7
Naked single: r4c13 = 4
Naked single: r7c16 = 1
Naked single: r8c13 = 7
Naked single: r8c15 = 6
Naked single: r10c15 = 1
hidden single in block: r3c3 = 4
hidden single in block: r1c7 = 4
hidden single in block: r7c2 = 4
hidden single in block: r12c13 = 13
hidden single in block: r7c3 = 2
hidden single in block: r5c14 = 13
hidden single in block: r5c13 = 12
hidden single in block: r3c14 = 12
hidden single in block: r2c14 = 16
hidden single in block: r3c7 = 16
hidden single in block: r1c13 = 11
hidden single in block: r16c14 = 11
hidden single in block: r2c7 = 10
hidden single in block: r2c9 = 11
hidden single in block: r3c13 = 10
hidden single in block: r14c6 = 11
hidden single in block: r16c16 = 6
hidden single in block: r7c8 = 11
hidden single in block: r14c5 = 10
hidden single in block: r6c6 = 10
hidden single in block: r13c5 = 4
hidden single in block: r15c6 = 8
hidden single in block: r16c11 = 4
hidden single in block: r16c10 = 14
hidden single in block: r2c11 = 14
hidden single in block: r6c5 = 8
hidden single in block: r14c1 = 4
hidden single in block: r14c3 = 6
hidden single in block: r14c2 = 8
hidden single in block: r16c2 = 16
hidden single in block: r13c8 = 16
hidden single in block: r14c12 = 16
hidden single in block: r2c3 = 8
hidden single in block: r4c2 = 14
hidden single in block: r4c10 = 7
hidden single in block: r5c8 = 6
hidden single in block: r7c6 = 7
hidden single in block: r5c12 = 7
hidden single in block: r6c9 = 16
hidden single in block: r12c1 = 8
hidden single in block: r15c3 = 1
hidden single in block: r15c9 = 2
hidden single in block: r2c2 = 7
hidden single in block: r3c11 = 1
hidden single in block: r12c3 = 7
hidden single in block: r16c1 = 2
hidden single in block: r15c1 = 5
hidden single in block: r14c7 = 2
hidden single in block: r9c5 = 2
hidden single in block: r12c5 = 6
hidden single in block: r4c6 = 6
hidden single in block: r8c6 = 2
hidden single in block: r11c2 = 2
hidden single in block: r9c2 = 5
hidden single in block: r10c12 = 2
hidden single in block: r4c5 = 1
hidden single in block: r8c8 = 1
hidden single in block: r8c5 = 5
hidden single in block: r11c7 = 1
hidden single in block: r12c8 = 5
hidden single in block: r9c7 = 7
hidden single in block: r12c9 = 1
hidden single in block: r10c16 = 5
hidden single in block: r10c14 = 7
hidden single in block: r12c16 = 15
hidden single in block: r16c6 = 1
hidden single in block: r13c7 = 5
hidden single in block: r16c8 = 7
hidden single in block: r14c10 = 5
hidden single in block: r14c13 = 1
hidden single in block: r16c13 = 5
hidden single in block: r11c11 = 7
hidden single in block: r9c14 = 6
hidden single in block: r13c12 = 1
hidden single in block: r13c11 = 6
hidden single in block: r13c9 = 7
hidden single in block: r6c10 = 1
hidden single in block: r6c12 = 6
hidden single in block: r11c12 = 5
hidden single in block: r11c10 = 6
hidden single in block: r10c11 = 15
hidden single in block: r7c11 = 5
hidden single in block: r7c12 = 15
hidden single in block: r10c1 = 6
hidden single in block: r11c1 = 15
hidden single in block: r10c9 = 10
hidden single in block: r1c9 = 5
hidden single in block: r1c11 = 10
sudoko0815

Posts: 3
Joined: 03 July 2017

### Re: minimum number of clues 16x16 and higher

sudoko0815 wrote:after 28 ms. The puzzle is very easy since it uses only hidden and naked singles: Her the "raw" output, numbers 0..F are translated to 1..16:

The puzzle as published is not minimal. Removing 11 clues yields a minimal, hard, puzzle (with 0 as 16, A as 10, ... F as 15):
Code: Select all
`  .  5  .  .  6  .  . 14  . 15  . 12  . 16  .  . 11  .  . 16  2  4  .  .  .  1  .  3  5  . 14  .  .  .  .  .  . 13  .  1  5  .  .  .  .  .  .  .  .  .  9 15  .  . 12  .  .  .  2  .  .  4  .  8  . 16  2  . 15  3 14  .  .  9  7  .  .  .  4  .  6 12  4 13  .  .  .  .  .  .  .  . 14  2  .  .  .  .  .  5  .  .  .  . 11  8  .  .  7 13 15  .  .  .  .  .  .  . 13  .  3  . 10  .  .  .  .  9 16  .  .  .  . 14  . 12  . 11  .  .  .  .  . 15  .  2 13 12  .  .  7  3  .  .  .  .  8  .  .  .  .  . 15  3  .  8  .  .  .  .  .  .  2  7 11 10  .  8  .  .  .  2 10  .  .  . 15 13  .  1  9  . 13 10 11  .  .  .  .  .  . 14  .  .  1  9  .  .  .  .  .  .  .  .  .  2  8  . 12  .  .  . 13  .  .  9  .  .  8  .  .  .  .  .  . 10 15  .  .  6  .  . 12  .  .  . 11  .  7  .  .  .  .  .  2  .`

Regards,

Mike Metcalf

P.S. The smallest number of clues for a 16x16 was reported by gsf as 77 here. My own best was 84 clues.

P.P.S. This topic belongs in the Variants thread! m_b_metcalf
2017 Supporter

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Joined: 15 May 2006
Location: Berlin

### Re: minimum number of clues 16x16 and higher

coloin

Posts: 2237
Joined: 05 May 2005
Location: Devon