eleven wrote:Obviously things are more complex than i thought.
The next thing is, that if i calculate the non-equivalents for the first 2 boxes with the 21 clue (like i did for the 20 clue), i get more (494508 vs 306283).
At least one reason is, that the 21 introduces a 5th number from the beginning.
So i get many new sub-puzzles with an addidional digit (which would be eqivalents without the new clue).
When i added the next digit then, the new symmetry only eliminated about 10% of the puzzles (293056 of 3461556).
I let them in to enumerate the puzzles in the same way as for the 20 clue. The result was 175 bio (minus about 10% ?) , which is much more than the 101 bio, i had for the 20 clue.
These numbers are not exact because of remaining equivalents and maybe bugs, but now i assume, that the 21 search would last longer.
Hi eleven,
No surprise if I disagree with your post. Facts seem against your findings, so the question is why??
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First of all, back to the question does the 21 clues pattern contains the 20 clues puzzles.
The final answer is 'yes', but we can add that, as the puzzle has a unique solution, it generates only one puzzle in the 21 clues pattern.
What is not granted is that the canonical form in the 21 clues pattern will fit with the 20 clues pattern.
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Now back to the count.
Skipping from 20 clues to 21 clues, we add symmetries. this is a special situation and the count (and the process) has to try to take care of that.
The general strategy, to get the best of the symmetry is to generate first cells having all the symmetries.
Here we get all the symmetries using in a first step rows 1 3 7 9 (8 cells).
The next "good step", to compare both way is to work on box 5.
I first took all clues in that box and got the comparative result already shown:
57990 seeds in 20 clues mode
54339 seeds in 21 clues mode
At that point, 2 remarks.
We are nearly equal for the future (still 8 cells to generate), with a small advantage to the 21 clues pattern with one more assigned
At the end, the new symmetries overcompensated the extension to one more clue.
In fact, cell r5c5 does not contribute to the reduction, so in my final test, I started with 12 cells in 21 clues mode and 15446 seeds.
In the partial treatment you made, you did not at all had benefit of the main symmetry
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the facts subject to a final check that the process is working properly
I prepared 5 batches extending the "pre generation" to 16 clues.
The compression ratio in the third step (filling boxes 1 3 7 9) has been 13%
Each batch contains in average a little more than 2 million puzzles.
5 digits are still unknown including the central digit in box 5.
I started one batch yesterday at noon. It should be covered at more than 2/3 in 24 hours (now quarter to nine)
I started a second batch 13 hours ago and it is covered at more than one third.
At the end, this seems roughly twice as fast as the 20 clues search.
champagne
