ronk wrote:...

dobrichev, many of the 39s are not close neighbors. What caused you to choose

this close pair

Red Ed wrote:dobrichev wrote:Can repeat and obtain transformations if there is interest.

Yes please.

I'm interested as well.

Unfortunately the

example was wrong. Sorry.

I didn't choose a pair, but run the program against a list of 75 known 39s. It should process each puzzle and print the similar ones. I messed up the puzzle lists so the program processed the second puzzle and found its isomorph but wrongly displayed it as a transformation of the first puzzle (which is in another list, ordered differently).

Nevertheless I got some similar results.

I ran the "relabel 3 clues", w/o +1/-1, against the same list. Here are the results.

- Code: Select all
`103056709056009002709210605210030500307065200065120308000000000000091807071000903`

103056709406709103790100500065004007304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[35]=9

103056709056009002709210605210030006307065200065120308000091807000000000071000903

103056709406709103790100500065004900304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[33]=7

103056780056080020708201560210003050307065200065102390000000000000018970071000830

103056780400780100708013064205870046004035870800604050302000610501360000000000000

c[18]=8,c[20]=7,c[45]=7

103056780056080020708201560210003600307065200065102390000018970000000000071000830

103056780400780100708013064205870046004035870007604050302000610501360000000000000

c[18]=8,c[20]=7,c[47]=8

103056780400780100708013064205870046004035870800604050302000610501360000000000000

103056780056080020708201560210003050307065200065102390000000000000018970071000830

c[24]=6,c[25]=5,c[34]=6

103056780400780100708013064205870046004035870007604050302000610501360000000000000

103056780056080020708201560210003600307065200065102390000018970000000000071000830

c[24]=6,c[25]=5,c[33]=5

120400780406700100780102064208305610000000000630201058370004800804003070062007040

120400780406700100780102064208301650000000000630205018370004800804003070062007040

c[0]=5,c[15]=5,c[21]=5

120400780406700100780102064208301650000000000630205018370004800804003070062007040

120400780406700100780102064208305610000000000630201058370004800804003070062007040

c[0]=5,c[15]=5,c[21]=5

103056709406709103790100500065004900304907005970065204000000000630000401000601302

103056709056009002709210605210030006307065200065120308000091807000000000071000903

c[24]=5,c[26]=6,c[35]=5

103056709406709103790100500065004007304907005970065204000000000630000401000601302

103056709056009002709210605210030500307065200065120308000000000000091807071000903

c[24]=5,c[26]=6,c[33]=6

The transformations are in ugly form (sorry again) and must be read as follows.

Apply the transformation from the third row to the min-row-lex normalized puzzle on the second row.

Then min-row-lex normalize the transformed puzzle and you will get the result on first row.

c[6]=9 means relabel cell at zero based position 6 to value of 9 .

In other words, the puzzle at first row can be obtained from the puzzle from second row, applying the transformation at third row. Both puzzles are in row-min-lex format.

So, these pairs are at Hamming distance of 3. Up to errors

.

Next, I ran "relabel 3 then apply -1/+1". This time against a list of 82 known 39s.

Calculation is still in progress, ~14 minutes per puzzle @ 2.8 GHz.

Here are the results for the first 8 puzzles.

- Code: Select all
`003400700450780020780023460038090640600308950900000000070800290090032070802970530`

c[10]=1,c[43]=1,c[78]=1,c[67]=0,c[54]=3

003400700410780020780023460038090640600308910900000000370800290090002070802970130

003400700450780020780023460038090640600308950900000000370800290090002070802970530

003400700450780020780023460038090640600308950900000000070800290090032070802970530

c[25]=1,c[33]=1,c[36]=1,c[67]=0,c[54]=3

003400700450780020780023410038090140100308950900000000370800290090002070802970530

003400700450780020780023460038090640600308950900000000370800290090002070802970530

.

003400700450780020780023460038090640600308950900000000370800290090002070802970530

c[10]=1,c[43]=1,c[78]=1,c[54]=0,c[67]=3

003400700410780020780023460038090640600308910900000000070800290090032070802970130

003400700450780020780023460038090640600308950900000000070800290090032070802970530

003400700450780020780023460038090640600308950900000000370800290090002070802970530

c[25]=1,c[33]=1,c[36]=1,c[54]=0,c[67]=3

003400700450780020780023410038090140100308950900000000070800290090032070802970530

003400700450780020780023460038090640600308950900000000070800290090032070802970530

.

003400700450780020780023460038090640600308950900000000090800270070032090802970530

c[10]=1,c[43]=1,c[78]=1,c[67]=0,c[54]=3

003400700410780020780023460038090640600308910900000000390800270070002090802970130

003400700450780020780023460038090640600308950900000000390800270070002090802970530

003400700450780020780023460038090640600308950900000000090800270070032090802970530

c[25]=1,c[33]=1,c[36]=1,c[67]=0,c[54]=3

003400700450780020780023410038090140100308950900000000390800270070002090802970530

003400700450780020780023460038090640600308950900000000390800270070002090802970530

.

003400700450780020780023460038090640600308950900000000390800270070002090802970530

c[10]=1,c[43]=1,c[78]=1,c[54]=0,c[67]=3

003400700410780020780023460038090640600308910900000000090800270070032090802970130

003400700450780020780023460038090640600308950900000000090800270070032090802970530

003400700450780020780023460038090640600308950900000000390800270070002090802970530

c[25]=1,c[33]=1,c[36]=1,c[54]=0,c[67]=3

003400700450780020780023410038090140100308950900000000090800270070032090802970530

003400700450780020780023460038090640600308950900000000090800270070032090802970530

...

103056709406709103790100500065004007304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[35]=8,c[35]=0,c[33]=7

103056907406709103790100500065004700304907005970065204000000000630000401000601302

103056709056009002709210605210030006307065200065120308000091807000000000071000903

103056709406709103790100500065004007304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[35]=9

103056907406709103790100500065004009304907005970065204000000000630000401000601302

103056709056009002709210605210030500307065200065120308000000000000091807071000903

103056709406709103790100500065004007304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[35]=1,c[35]=0,c[33]=7

103056907406709103790100500065004700304907005970065204000000000630000401000601302

103056709056009002709210605210030006307065200065120308000091807000000000071000903

103056709406709103790100500065004007304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[35]=2,c[35]=0,c[33]=7

103056907406709103790100500065004700304907005970065204000000000630000401000601302

103056709056009002709210605210030006307065200065120308000091807000000000071000903

103056709406709103790100500065004007304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[35]=3,c[35]=0,c[33]=7

103056907406709103790100500065004700304907005970065204000000000630000401000601302

103056709056009002709210605210030006307065200065120308000091807000000000071000903

103056709406709103790100500065004007304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[35]=4,c[35]=0,c[33]=7

103056907406709103790100500065004700304907005970065204000000000630000401000601302

103056709056009002709210605210030006307065200065120308000091807000000000071000903

103056709406709103790100500065004007304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[35]=5,c[35]=0,c[33]=7

103056907406709103790100500065004700304907005970065204000000000630000401000601302

103056709056009002709210605210030006307065200065120308000091807000000000071000903

103056709406709103790100500065004007304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[35]=6,c[35]=0,c[33]=7

103056907406709103790100500065004700304907005970065204000000000630000401000601302

103056709056009002709210605210030006307065200065120308000091807000000000071000903

.

103056709406709103790100500065004900304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[33]=1,c[33]=0,c[35]=9

103056907406709103790100500065004009304907005970065204000000000630000401000601302

103056709056009002709210605210030500307065200065120308000000000000091807071000903

103056709406709103790100500065004900304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[33]=2,c[33]=0,c[35]=9

103056907406709103790100500065004009304907005970065204000000000630000401000601302

103056709056009002709210605210030500307065200065120308000000000000091807071000903

103056709406709103790100500065004900304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[33]=3,c[33]=0,c[35]=9

103056907406709103790100500065004009304907005970065204000000000630000401000601302

103056709056009002709210605210030500307065200065120308000000000000091807071000903

103056709406709103790100500065004900304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[33]=4,c[33]=0,c[35]=9

103056907406709103790100500065004009304907005970065204000000000630000401000601302

103056709056009002709210605210030500307065200065120308000000000000091807071000903

103056709406709103790100500065004900304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[33]=5,c[33]=0,c[35]=9

103056907406709103790100500065004009304907005970065204000000000630000401000601302

103056709056009002709210605210030500307065200065120308000000000000091807071000903

103056709406709103790100500065004900304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[33]=6,c[33]=0,c[35]=9

103056907406709103790100500065004009304907005970065204000000000630000401000601302

103056709056009002709210605210030500307065200065120308000000000000091807071000903

103056709406709103790100500065004900304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[33]=7

103056907406709103790100500065004700304907005970065204000000000630000401000601302

103056709056009002709210605210030006307065200065120308000091807000000000071000903

103056709406709103790100500065004900304907005970065204000000000630000401000601302

c[6]=9,c[8]=7,c[33]=8,c[33]=0,c[35]=9

103056907406709103790100500065004009304907005970065204000000000630000401000601302

103056709056009002709210605210030500307065200065120308000000000000091807071000903

.

The rows are: take the puzzle from line 1, apply transformation from line 2, and you get the new puzzle at line 3, which is isomorph of the puzzle at line 4.

Now some fun from the first puzzle.

c[10]=1,c[43]=1,c[78]=1,c[67]=0,c[54]=3 actually means

"replace all occurrences of "5" with "1", then apply -1 at pos 67 and +1 at pos 54". The relabeling is unnecessary, and the actual Hamming distance is 2. That is side effect because I assumed a cheaper transformations are already done at previous steps, and a "black list" with knowns is formed. For these experiments I excluded the black list and each puzzle is compared only to itself to avoid outputting the isomorphs.

MD