Shintaro wrote:I think we need to agree on the definition of equivalent puzzles before we start solving the puzzle. Do you all agree with me...

Yes, of course, that is part of the basic definition of equivalent puzzles. As I said you may also permutate the grid by swapping the rows/columns within the bands/stacks, but apparently that's not part of this game?

Shintaro wrote:If nobody can get the solution, it means that there is a flaw in the design of the puzzle, and more starting digits are required for both grids.

The puzzle is valid, here's the solution in canonical form:

123457689456189327789623415264538791537916842918742563371264958695871234842395176

It's the only solution that satisfies both grids. This was found by comparing all solutions of both puzzles, which of course isn't a very neat way of doing it. I'm not sure if I understand your instructions here:

Shintaro wrote:In other words, we must try to locate at least two equivalent blocks that have been shifted to their new position in twin B.

Under the basic permutation rules, any block can be equivalent to any other block. Also any two blocks can be equivalent to any other two blocks, if they don't share a band or stack, so the two blocks you are talking about should be in the same chute, or? I couldn't see any such relationship between two blocks, but maybe someone else can...

RW