JPF wrote:How do you get 78 bits ?

Starting from the locked pattern, first placing digit 1 as in udosuks example:

- Code: Select all
`123|4--|... `

456|...|...

789|...|4..

---+---+---

|4.|...|...

|..|...|.4.

|..|..4|...

---+---+---

..4|...|...

...|.4.|...

...|...|..4

In box 4, 5 options=3 bits, box 2, 6 options=3 bits. Then boxes 6 and 8, also 3 bits each, finally box 9 requires only 2 bits. That's 14 bits for digit 1.

- Code: Select all
`123|4..|... `

456|...|...

789|-1-|4..

---+---+---

|4.|...|...

|.1|...|.4.

|..|..4|..1

---+---+---

..4|...|.1.

...|14.|...

...|...|..4

Next, go for digit 7. Max 4 possibilities in box 4 = 2 bits, the other boxes as digit 1, total of 13 bits for digit 7.

- Code: Select all
`123|4.7|... `

456|...|...

789|.1.|4..

---+---+---

.4.|...|7..

.71|...|.4.

...|..4|..1

---+---+---

..4|.7.|.1.

...|14.|..7

...|...|..4

Next, digit 8, max 4 options in box 2, otherwise as digit 1 => 13 bits. Digit 9 is done in the same way, 13 bits.

- Code: Select all
`123|4.7|... `

456|98.|...

789|.1.|4..

---+---+---

84.|...|7..

.71|...|.49

9..|..4|8.1

---+---+---

..4|.7.|.18

...|14.|.97

...|8.9|..4

From now on there can be max 4 possibilities for any digit, the next two digits can be solved in 5*2bits each.

After that there's max 2 possibilities left, the 8th digit can be solved in 5 bits, and the last one comes for free. That's 14+3*13+2*10+5=78 bits.

This should work on any grid, and all grids can be done in the same order to get the same 78 bit format. If we instead start with box 1 + all digits 1 locked and then proceed in numerical order, we would reach 80bits/grid.

RW