You are given a 9x9 grid of numbers such that:
a. each row,
b. column,
and
c. each of the nine 3x3 grids
has each number 1 through 9 exactly once.
Lets call it Sudoku puzzle's solution or SPS.
A grid with condition c. removed is called a Latin Square, LS.
1. (d2) how many 9x9 LS's are there?
2. (d4) And how many 9x9 SPS's ?
(In reply to
solution (part 1 only) by Steven Lord)
I can see the logic and don't see any flaws.
However, Sloane's OEIS
A002860 Number of
Latin squares of order n; or labeled quasigroups.
shows the 9th element as
5524751496156892842531225600
That's about 5.5 x 10^27
I don't see where the extra possibilities come from.
Modification:
Now I do see where the extras come from.
Say you are placing the 3's. According to the logic presented here, you would have a choice of 7 places in the top row (unoccupied by either 1 or 2), 6 places in the second row (unoccupied by 1 or 2 and not under a preceding 3), etc. However in some instances a preceding row's 3 may be in the same column as one already restricted by 1 or 2, so that does not further reduce the available columns. This gets more prevalent as you get further down and as you get to higher numbers.
Edited on July 14, 2018, 3:51 pm
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Posted by Charlie
on 2018-07-14 15:35:08 |
re: solution (part 1 only)
