Logic Masters Deutschland e.V.

This one, I think, is a bit of wolf in sheep clothing. I think it starts off easily enough, but there are a couple of quite tough logic options that need spotting to complete this.

Rules.

Classic sudoku rules apply.

The blue lines sums (totals) are squared values (eg 4,9,16 etc). Values to be determined.

The green lines are palindromes.

In addition, if a line has a 2 digit number in the corner, this means that the first x cells of the line (tens digit) total to the same value as the last y digits of the line (the unit value). Lines without the 2 digit value do not balance in this way.

Eg. On a line of 2,8,3,5,1,4 a value of 23 means that the first 2 digits from that side have the same total as the farthest 3 digits.

Penpa+ version with answer check here

CTC version with solution check here

Image of solution here

Happy solving

If you get stuck there are some 'get going' hints below. DO NOT read further unless you want those hints!

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Box1 and 6 clues:

Box1 can be completed immediately. The 1 in r1,c1 goes with a 3 as it cannot be an 8. The 3 digit line from r3,c1 MUST be a 16 total as the '12' clue means the '1' part must be half of the total, so cannot be an odd number and the minimum is 2,4,5 so 4 is out. The remainder cannot be 1/7 or 3/5 so must be a 2/6 combo. (Same goes for clue at r5,c7 (box 6) - the '1' part must be an 8 as 10 is the minimum line total and 36 is not attainable.) Also, in box 1, if the above is worked out the remaining line at r1,c3 MUST also be a 16 total. If it were a 9, then the box total would be 4+16+9 = 29. This needs a 9,7 to complete the box, but that's impossible as 1 of the 2 remaining cells can neither be 7 or 9 because of the givens.

Box 2 clues:

The given 1's show the box 2 line of length 3 must've a 1 in it, so it must be a 3,1,5. From this, and other givens, the rest of the box can be worked out as there is only 1 remaining combination that works.

That's it for clues. There are a couple of fairly hard logic jumps later in the puzzle, good luck.