This one's a toughie but it's also completely logical. I figure lots of you have some free time this holiday weekend. So sharpen your pencils and crack your knuckles and have some fun.

The digits 1-9 each appear four times in the grid, and no two squares which are adjacent horizontally or vertically contain the same digit. Every instance of a digit's occurring more than once in a row or column is mentioned in the clues.



ROWS
1. A pair of 8s enclosing a 5; total is 30
2. A pair of 1s; all the numbers are odd
3. A pair of 4s with 7 the highest number; total is 26
4. A pair of 6s; total is 41
5. A pair of 1s enclosing a 5; total is 23
6. A pair of 2s; total is 34

COLUMNS
1. A pair of 9s; total is 43
2. A pair of 3s with 8 the highest number; total is 28
3. A pair of 7s; all other numbers are even
4. A pair of 5s and a pair of 1s; total is 22
5. A pair of 9s but no 4s; total is 36
6. A pair of 1s but no 5s; total is 17

For clarification:

1: A pair of 8s enclosing a 5; total is 30
Does that mean they are consecutive, like ?585?, or not, like 5??85 or 5?8?5

And CCb crushes it! Well done!

Denis, yes. In your example, it would mean 585 with no other numbers between them.

Thanks. I had (in R1) 5 in C4 and 8 in C5,
so obviously there was an 8 left of the 5,
hence my question.

VERY delightful puzzle!

I started by getting R2's total: 180-30-26-41-23-34 = 26;
next similarly for C3: 180-43-28-22-36-17 = 34.

Congrats to CCb...also on getting Roman Coliseum...

Sue, was fiddling around with this.
It also has this slightly different solution:

4,2,8,5,8,3
9,5,7,1,3,1
6,3,7,4,2,4
7,8,6,5,9,6
9,3,4,1,5,1
8,7,2,6,9,2

The 2 7's in col3 are next to each other.
Couple other minor changes in bottom left quarter.
Once more: delightful little mudder!

Glad you enjoyed it, Denis. The two touching 7s disqualify it per the rules, but still a fun solve.

Whoopseedo, how did I miss this:
"...and no two squares which are adjacent horizontally
or vertically contain the same digit".

That little rule makes a huge difference when solving. Your solution is all the more impressive now.