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Knights circle the magical square, reading description needed

A German TV show has the battle of children against adults.
The child bet she can have a knight tour with a magical square in different numbers on each chessboard square faster than the adult.

So, she was blindfolded, had to start on a2, and a magical square target was selected randomly (406). The smallest possible one could have been 260.
Then she went to do the knight tour, naming the numbers and squares to move to.
Her opponent made only small mistakes, nearly also made a different magical square with the same target.
Karl Fabel woul have loved to see that.

https://www.youtube.com/watch?v=mHVt37juiwo - the actual action starts here: https://youtu.be/mHVt37juiwo?t=151

Bonus points if you understand German. Then you wouldn't have needed to read the description, but you name likely is Hauke Reddmann, so you expected some joke somewhere.
But I can only repeat one made in private a while back - with a different solution again:
Which singer likes fairy chess pieces? Andrea True Connection: "Moa, Moa, Moa"

I remember reading a similar article a while ago by some Indian(?) specialist who sent it to various outlets, including the Schwalbe, with different parts of his research. He also had some kind of magical squares with extra effects. Not sure if related, but someone will easily find and post it.

Awani Kumar.
Magic Knight tours expert.
His magic S-tours have been published in many chess problem and mathematics magazines.
E.g: https://arxiv.org/abs/1802.09340

As always on TV h1 is a dark square.

Listen to the stupid showmaster at minute 7:27
"Wenn's waagerecht keine Fehler gibt, kann's senkrecht keine geben."

What are the exact constraints, please?

The girl clearly has a specific magic square in mind. Then to each of the squares 47...56, she adds 4, and to the squares 57...64, she adds 142. Why do something as elaborate as that? Why not just add 146 to the squares 57...64? I don't understand. Or maybe it's because adding two variable numbers together 146+57...64 is error prone. If she knows that 142+57...64 = 199...206, then it's a lot easier arithmetically to add a variable 4+47...56. 200 is a nice round number.

Thanks,
Andrew

Every square can only be entered once in a knight tour.
Every number can only be named once.
The starting square and target number are randomly selected.
The participants are blindfolded.

EDIT @Shankar: Yes, that is the one I had meant!

(6) Posted by Andrew Buchanan [Saturday, Mar 19, 2022 08:02]

Thanks for this Siegfried. Since one can have a graeco-latin square of order 8 in which the major diagonals are also ok, it follows that the starting square value N could also be specified at the outset. As long as the total T >= 196+N, there will be a way to label the board happily. The knight’s tour does not add any additional mathematics but certainly ensures that the visualisation must be vivid in the contestant’s mind.