dobrichev wrote:To my understanding your puzzles are minimal, i.e. have no redundant clues.

I took the seventh puzzle and ... hit bugs in my software tools.

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`16.4..9.2..4..2..69.26..34..1.7.42.5.........2.58.6.3..81..75.97..5..8..5.9..8.73 #Leren's #7 with (wrong 7, likely 4) automorphisms`

168473952374952186952681347816734295437295618295816734681347529743529861529168473 #its solution with (wrong 14, likely 4) automorphisms

1 6 . 4 . . 9 . 2

. . 4 . . 2 . . 6

9 . 2 6 . . 3 4 .

. 1 . 7 . 4 2 . 5

. . . . . . . . .

2 . 5 8 . 6 . 3 .

. 8 1 . . 7 5 . 9

7 . . 5 . . 8 . .

5 . 9 . . 8 . 7 3 #Morph with 4x90deg rotational symmetry (+ other wrong symmetries = 7, but likely 4) automorphisms

168473952374952186952681347816734295437295618295816734681347529743529861529168473 #morph's solution with (wrong 12, likely 4) automorphisms

123456789456789123789123456231567894597834261864291537312678945678945312945312678 #minlex morph of the solution with 4? automorphisms

1..4..7....6.891.3..91.3.56.........5.78.4.6.8.4.9.5.7..2..8..56..94.3.29..3.267. #puzzle in minlex solution with 4? automorphisms

Assuming there is single error in the puzzle/solution automorphisms counting, and taking into account that puzzle automorphisms must be <= solution automorphisms, then both the puzzle and its solution should have 4x90 deg rotational symmetry only.

Can somebody confirm?

I confirm that

1. All 10 Leren's puzzles are minimal.

2. All 10 Leren's puzzles have 4 automorphisms each.

3. Solution grids for puzzles 3-10 have 4 automorphisms each, solution grids for puzzles 1-2 have 12 automorphisms each.

4. All 10 Leren's puzzles have neither quarter turn symmetry, nor double diagonal symmetry.

Serg