- Code: Select all
123456789
456789123
789123456
231564897
564897231
897231564
312645978
645978312
978312645
However, many of these digits are just redundant information... Because once we know 8 cells of each row/column we can deduce the 9th easily:
- Code: Select all
12345678.
45678912.
78912345.
23156489.
56489723.
89723156.
31264597.
64597831.
.........
Also, once we know 8 cells in a box we don't need to see the 9th... That means 4 more redundant digits...
- Code: Select all
12345678.
45678912.
78.12.45.
23156489.
56489723.
89.23.56.
31264597.
64597831.
.........
But that's not the end... Because if we fill in 8 boxes the 9th box must be determined... So we don't need to see the 4 digits in box 9 here...
- Code: Select all
12345678.
45678912.
78.12.45.
23156489.
56489723.
89.23.56.
312645...
645978...
.........
So 56 digits are what we need (so far)... That's about 2/3 of the initial information...
But can we do more? What I need is a template that when superimposed on any solution grid would still guarantee the solution stay unique...
Here is the symmetrical version of the 56-cell template we got so far:
- Code: Select all
.234.678.
4567.9123
7891.3456
231...897
.........
897...564
3126.5978
6459.8312
.783.264.
This issue has some practical value... Especially for people who store millions/billions of solution grids... I'm sure they wouldn't mind to free up 1/3 or even more of the space occupied!