Strategies for Popular Number Puzzles

Easiest Sudoku Competition

Just for fun and kudos, I am holding a competition for the 'easiest Sudoku puzzle'. Many people like to try their hand at creating Sudoku puzzles - and it's a fun process. But sometimes when you are searching for a difficult puzzle a dead easy one pops out. Now, instead of throwing it away, perhaps it can find a little glory on this page.

The rules are simple: The puzzle must have
  1. a single solution and
  2. a maximum of 31 clues
  3. beat the Eric Cole's Sudoku now in the solver as the 'Easiest Sudoku" - which scores 11. The grading must occur before you press "Take Step".
  4. Less clues beats same score entry with more clues

To be the current winner your puzzle must demonstrate a smaller grade (although I'd be happy to list equal winners). UPDATE: . Since 2 is concievably the lowest score, new winners will have to have less clues that than the current winner.

I'm very pleased to start this competition with an entry from Eric Cole in Oregon, USA, which scores 11. I have received excellent contributions from Will Gibson, David Filmer, lmars Cirulis and Mats Anderbok. You can load their puzzles by clicking on them:

Joint Winner 16th December 2023, (Score 3, 31 clues), Ilmars Cirulis


Joint Winner 7th May 2010, (Score 3, 31 clues), Ilmars Cirulis


Winner 25th October 2009, (Score 4, 31 clues), David Filmer

Winner 15th June 2010, (Score 4, 31 clues), David Filmer

Winner 10th October 2009, (Score 4), Mats Anderbok

Winner 5th June 2009, (Score 6), Will Gibson

Winner 29th May 2009, (Score 6), Tobias Santschi

Winner 18th May 2009, (Score 6), Will Gibson

First Winner (Score 11), Eric Cole , 6th May 2009

Send your entries to me via the Feedback form.

Best of luck!

Andrew Stuart



... by: Ilmars

Friday 5-Nov-2010

For the puzzle with 31 clues - 22/21/7
For the puzzle with 30 clues - 19/19/13

... by: Ilmars

Friday 5-Nov-2010
--- At first, something for fun.
The puzzle 014000000009700605080002730205001004070050000600397008000680310097400080000005029 (with 32 clues) is solved in three rounds by solver - with number of solved cells in each 22/23/4.

Can someone find a puzzle with 32 clues which can be solved in two rounds?

--- Next...
How exactly are calculated the simplicity (grade) of such simple puzzles which can be solved only by solved cells? I feel such lack of knowledge not good for searching of easiest puzzles and also not good for confidence about precisity of grader. I feeling confused.

--- Finally, the grader got flu or something similar. Now the easiest puzzles have grade no 1, but 13 or similar. I hope that it is change only in number, not in diference between two puzzles (i mean, one puzzle is harder than another both with old grader and the "new").

Also because I found puzzle with 30 clues and "new" grade 11 - which is better than puzzle of David. :) But it is more for fun, not for founding really easiest puzzle - yes, because I'm confused about calculation of grade.

--- PS.
I will post also puzzles for 31 and 30 clues which have fewest rounds (solving by solver) and bigger number of cells in first rounds. Again for fun - who can make better? :)

-- 31 clues --
-- 30 clues --

... by: David Filmer MA (Cantab)

Saturday 21-Aug-2010
Wedding Sudoku: Grade 1 and only 30 clues!

Hello Andrew and fellow Sudoku creators.

It's my 55th Wedding Anniversary and a wet Saturday morning, so I am submitting one of several Sudokus I did that beat previous winners as under: -


This can also be set out as follows:


I have been working with Mats Anderbok (also a previous winner) on a simple method of solving gentle sudokus using a strategy advocated by the late Michael Mepham. Instead of normal computer methods, this works like a human where one cell is solved AND ENTERED at a time. I worked out the logic and Mats made an excellent job of the programming in just 2 days! An advantage is that no "Candidate numbers" are entered: the correct solution is entered directly.

The following print out shows how, and the order in which, each of the 51 blank cells is solved


[31,1] to [81,1]
"[31-81" shows the first/last cell solved : ",1]" shows the grade to date

SS1 (Subset) Total 6. SS1=Col 1-3: 3=Col 7-9: 4=Row A-C: 6=Row G-J

V0-V3: No of times a number occurs in a subset.V3=3:V2=2:V1=1:V0=0

You will see from the following, that the Grade on this method is also 1.


[31,1] SS1 V2: A intercept, B2 occupied: SOLUTION: 4 (C2)
[32,1] SS1 V2: J intercept, H2 occupied: SOLUTION: 5 (G2)
[33,1] SS1 V2: A intercept, B1 occupied: SOLUTION: 7 (C1)
[34,1] SS1 V2: D intercept, E1 occupied: SOLUTION: 8 (F1)
[35,1] SS1 V1: E,F intercept, D3 occupied: SOLUTION: 1 (D1)
[36,1] SS1 V1: C intercept, A3,B1,B3 occupied: SOLUTION: 3 (A1)
[37,1] SS1 V1: E,1 intercept, D3 occupied: SOLUTION: 3 (F3)
[38,1] SS1 V1: D intercept, E1,F1,F2 occupied: SOLUTION: 6 (E2)
[39,1] SS1 V1: G,2 intercept, J1 occupied: SOLUTION: 6 (H1)
[40,1] SS1 V1: C intercept, A3,B2,B3 occupied: SOLUTION: 9 (A2)
[41,1] SS1 V1: G,2 intercept, J3 occupied: SOLUTION: 9 (H3)
[42,1] SS1 V0: B intercept, A1,A2,A3,C1,C2 filled: SOLUTION: 2 (C3)
[43,1] SS1 V0: F,3 intercept, D1,E1,E2 occupied: SOLUTION: 2 (D2)
[44,1] SS1 V0: 2,3 intercept, H1,J1 occupied: SOLUTION: 2 (G1)
[45,1] SS1 V2: No intercept, H3,J3 occupied: SOLUTION: 1 (G3)
[46,1] SS2 V2: G intercept, J4 occupied: SOLUTION: 2 (H4)
[47,1] SS2 V2: E intercept, F4 occupied: SOLUTION: 9 (D4)
[48,1] SS2 V1: E,F intercept, D4 occupied: SOLUTION: 3 (D6)
[49,1] SS2 V1: J,6 intercept, H4 occupied: SOLUTION: 3 (G4)
[50,1] SS2 V1: A,C intercept, B5 occupied: SOLUTION: 4 (B6)
[51,1] SS2 V1: J,6 intercept, G5 occupied: SOLUTION: 4 (H5)
[52,1] SS2 V1: B,C intercept, A6 occupied: SOLUTION: 5 (A5)
[53,1] SS2 V1: D,5 intercept, F6 occupied: SOLUTION: 5 (E6)
[54,1] SS2 V1: A,C intercept, B5 occupied: SOLUTION: 7 (B4)
[55,1] SS2 V1: F,4 intercept, E5 occupied: SOLUTION: 7 (D5)
[56,1] SS2 V1: D,F intercept, E5 occupied: SOLUTION: 8 (E4)
[57,1] SS2 V1: H,4 intercept, G5 occupied: SOLUTION: 8 (J5)
[58,1] SS2 V0: D,E intercept, F4,F6 occupied: SOLUTION: 6 (F5)
[59,1] SS2 V0: A,5 intercept, B4,B6,C6 occupied: SOLUTION: 6 (C4)
[60,1] SS2 V0: G,H,4,5 intercept: SOLUTION: 6 (J6)
[61,1] SS2 V1: B intercept, A6,C4,C6 occupied: SOLUTION: 1 (A4)
[62,1] SS2 V1: G,4 intercept, J6 occupied: SOLUTION: 1 (H6)
[63,1] SS3 V2: A,C intercept: SOLUTION: 6 (B7)
[64,1] SS3 V1: A,B intercept, C7 occupied: SOLUTION: 1 (C9)
[65,1] SS3 V1: G,H,9 intercept: SOLUTION: 1 (J7)
[66,1] SS3 V1: A,C intercept, B7 occupied: SOLUTION: 3 (B8)
[67,1] SS3 V1: G,J,8 intercept: SOLUTION: 3 (H7)
[68,1] SS3 V1: E,F intercept, D7 occupied: SOLUTION: 4 (D8)
[69,1] SS3 V1: H,J,8 intercept: SOLUTION: 4 (G7)
[70,1] SS3 V1: D,E intercept, F8 occupied: SOLUTION: 5 (F9)
[71,1] SS3 V1: G,J,9 intercept: SOLUTION: 5 (H8)
[72,1] SS3 V1: D,F intercept, E9 occupied: SOLUTION: 7 (E8)
[73,1] SS3 V1: G,J,8 intercept: SOLUTION: 7 (H9)
[74,1] SS3 V1: A,B intercept, C9 occupied: SOLUTION: 8 (C8)
[75,1] SS3 V1: H,J,8 intercept: SOLUTION: 8 (G9)
[76,1] SS3 V0: B,C intercept, A7,A9 occupied: SOLUTION: 2 (A8)
[77,1] SS3 V0: D,F,8 intercept, E9 occupied: SOLUTION: 2 (E7)
[78,1] SS3 V0: G,H,7,8 intercept: SOLUTION: 2 (J9)
[79,1] SS3 V0: A,C intercept, B7,B8 occupied: SOLUTION: 9 (B9)
[80,1] SS3 V0: D,E,9 intercept, F8 occupied: SOLUTION: 9 (F7)
[81,1] SS3 V0: G,H,7,9 intercept: SOLUTION: 9 (J8)

... by: Mats Anderbok, Sweden

Thursday 8-Oct-2009
Here are my contributions to your "competition" for easiest sudoku with 32 clues. I produced around 40 puzzles which scored 2 on your grader, and these are two of the easiest ones:
They can be solved in two rounds using all independent singles, or in three rounds using only naked singles. The number of solved are 36/49-18/39/49 and 35/49-20/38/49 after each round. It is probably possible to get score 2 with less than 32 clues or score 1 with 32, but I don't have the time and tools to investigate this further, because I don't know exactly how the grader computes the score.

May I suggest, as a different rule instead of the arbitrary 32 clues, that the puzzle should be minimal (no clue can be removed without multiple solutions)? It's kind of cheating to start with a valid sudoku and add digits to make it easier.

Method: Starting with a list of puzzles with 17 clues, I filled 15 random cells, and then counted the number of naked singles available. I suppose your grader views naked singles as easier than hidden (which I don't agree with as a general rule). From a total of more than 200 million generated, I tested around 5000 on the grader, most of them scoring 4-8. This is a tedious task, even if I don't do it manually, because using the grader over the web takes a few seconds for each puzzle (I apologize for the server work load). In all, it took me two days.

Note: It is not always true that a "partially completed puzzle will have an easier grade", at least not a lower or equal score. This example has two additional clues and scores 4, which shows how hard it is to implement a good grading algorithm.


... by: David Filmer

Saturday 26-Sep-2009
In your introduction to this competition you say "I'd be happy to list equal winners".
May I therefore submit the following, which also has a grade of 3.
Will Gibson's entry solves in 4 rounds when you click on "Take Step". In turn, the 4 steps solve 14, 11, 18 and 6 cells.
If you do the same for my entry, the 4 steps solve 14, 22, 12 and 1 cell in turn, so in that respect, I think that mine is easier although the grade is the same. I have produced a Sudoku which grades 2, but it has 33 clues, so breaks the rules. I am still struggling to find a Grade 2 Sudoku with 32 clues!
David Filmer
Article created on 9-May-2009. Views: 38695
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