- 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!