1 2 3 | 3 8 4 | 7 8 9
4 5 6 | 8 6 9 | 1 3 3
7 8 9 | 1 1 5 | 4 4 6
-----------------------
2 3 1 | 5 6 4 | 8 9 7
5 6 4 | 8 9 7 | 2 3 1
8 9 7 | 2 3 1 | 5 6 4
-----------------------
3 1 2 | 6 4 5 | 9 7 8
6 4 5 | 9 7 8 | 3 1 2
9 7 8 | 3 1 2 | 6 4 5
Animator wrote:Actually you can have the number 45 for each box, row and column and have an incorrect grid. Ofcourse it requires that you made more then one mistakes, but that is usually the case ...
Take this incorrect grid for example:1 2 3 | 3 8 4 | 7 8 9
4 5 6 | 8 6 9 | 1 3 3
7 8 9 | 1 1 5 | 4 4 6
-----------------------
2 3 1 | 5 6 4 | 8 9 7
5 6 4 | 8 9 7 | 2 3 1
8 9 7 | 2 3 1 | 5 6 4
-----------------------
3 1 2 | 6 4 5 | 9 7 8
6 4 5 | 9 7 8 | 3 1 2
9 7 8 | 3 1 2 | 6 4 5
I'm not 100% sure with what you mean with the following sentence: 'the count must be 9 (number of numbers).' Do you mean: that there must be 9 different numbers, or that there simply should be 9 numbers. (In the second case it is irrelevant wheter or not there are duplicates numbers in a row)
Animator wrote:Summing 1², 2², ... will be a lot tricker to fool, but I'm not sure that it is impossible...
1 2 3 | 2 3 8 | 7 8 9
4 5 6 | 7 8 9 | 1 2 3
7 8 9 | 1 2 3 | 4 5 6
-----------------------
5 6 4 | 8 9 7 | 2 3 1
2 3 1 | 3 8 2 | 8 9 7
8 9 7 | 2 3 1 | 5 6 4
-----------------------
6 4 5 | 9 7 8 | 3 1 2
3 1 2 | 8 2 3 | 9 7 8
9 7 8 | 3 1 2 | 6 4 5