Maya Cosmic Number Puzzles

[MCNP2010]

00 __ __ __ 56 __ 42
__ 11 __ 04 __ __ __
__ __ __ __ 15 __ 01
__ 40 __ 33 __ 26 __
65 __ 51 __ __ __ __
__ __ __ 62 __ 55 __
24 __ 10 __ __ __ 66

Rules
1. No first digit is repeated in any row or column.
2. No Second digit is repeated in any row or column.
3. No two digit combination is repeated.
Note: This puzzles the numbers 0-6.

This is a simple example puzzle.
Can you fill in the blanks?
Stephen

[jaap]

I used pen & paper. Although each step in the solve was easy, those steps are hard to spot. I needed to make lots of annotations, and it is easy to make so many that it becomes a big unreadable mess.

Spoiler:

Code: Select all

00 35 63 21 56 14 42
53 11 46 04 32 60 25
36 64 22 50 15 43 01
12 40 05 33 61 26 54
65 23 51 16 44 02 30
41 06 34 62 20 55 13
24 52 10 45 03 31 66

[MCNP2010]

The easiest way is to take a column or row, figure out what is needed for the first digit, do the same for the second digit, and then figure out what combinations are allowed. Sometimes there is a first digit that can only be combined with one of the second digits.
Try this. It should make it a little less messy.

[Tirear]

00 __ __ __ 56 __ 42
__ 11 __ 04 __ __ __
__ __ __ __ 15 __ 01
__ 40 __ 33 __ 26 __
65 __ 51 __ __ __ __
__ __ __ 62 __ 55 __
24 __ 10 __ __ __ 66

Rules
1. No first digit is repeated in any row or column.
2. No Second digit is repeated in any row or column.
3. No two digit combination is repeated.
Note: This puzzles the numbers 0-6.

This is a simple example puzzle.
Can you fill in the blanks?
Stephen

Spoiler:

The placement of the second digits are the same as the first digits flipped diagonally. This means that I can look at just one of the digits with the added rule combinations of numbers and their mirrors cannot repeat. The obvious implication is that the main diagonal has to contain all 7 numbers, as otherwise a palindrome would repeat. Do other diagonals share this requirement? Actually, doesn't it look like all diagonals occur in the same order? By assuming this pattern is real and connecting diagonals to get a length of seven, I get the following solution:
0362514
5140362
3625140
1403625
6251403
4036251
2514036
This seems to satisfy all of the rules.

[MCNP2010]

The spoiler is correct. That is why this is only a simple example. This puzzle is made from a self-orthogonal Latin square.

[generalz]

Cool puzzle! Fun to solve