Just released at Lybrary. Nice comment from Chris Wasshuber.

ULTIMATE MAGIC TOUR
by Michael Daniels

You know the chess knight tour effect. You know the magic square effect. Have you ever thought of combining the two? I have personally spent a lot of time developing innovative methods for both magic squares and the knight tour. But for some reason, I have never contemplated combining these two effects. It is an outrageous idea, because even a bit of cursory thinking of how that could be done leads one quickly to hard problems nobody has been able to solve ... until now. Michael Daniels has combined these two effects and has found a workable method that is simpler than you may think. If you like magic squares and/or knight tours, this is for you. Michael breaks new ground ...
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Chess savant effect

Ultimate Magic Tour allows the performer to complete the classic Knight's Tour Chess Challenge with no memory work or calculation and kicker predictions. Two effects are possible:

Basic (Non-magic) Tour
The spectator freely chooses one of the 64 squares on the 8x8 chessboard. The performer immediately writes a secret prediction and proceeds to make moves, numbering each square "1", "2", "3", etc., starting at the spectator's square, until all squares have been visited exactly once. Incredibly, the final square exactly matches the prediction.

Magic Tour
After completing the Basic Tour, the performer reveals that the written numbers make a "magic square" in which every row and every column on the chessboard add up to the same total, which the performer also predicted!

- Feature effect for mentalists, puzzlers, chess enthusiasts and math teachers.
- Completely self-contained - no other props, cribs or technology needed.
- Instantly repeatable with different starting squares and outcomes.
- Instructions and hi-res chessboard artwork are included for two different presentations (Simple and Advanced).
- Print your own pocket-size chessboards for close-up and EDC.
- For larger sizes (suitable for parlor and stage) use commercial printing services. [Manufacturing rights reserved by the author]
- A bonus blindfold method is included (requires fully taught intermediate-level memory work).

$25 PDF
https://www.lybrary.com/ultimate-magic-tour-p-927792.html

On December 28, 2011, German memory mathemagician Robin Wersig appeared on the German TV show "Superhirn" and presented an 8x8 balanced instant magic square with a specified sum. He filled in the cells using a knight's tour. He won the show. I saw Robin's performance at the Mental Calculation World Cup 2010 in Magdeburg, where I presented the opening show.
https://www.spiegel.de/fotostrecke/super......905.html

In 2021, I published a booklet in German titled "Hans-Christian Solka - Magical Square IV, Fully Magical Knight's Tour; v 1_02," which features a Fully Magical Knight's Tour in which the audience specifies the starting board and the starting value.

Thanks for this hcs. Great to hear that others have attempted this feat.

From what I can gather from the article in Der Spiegel, although Wersig may have been written the numbers in the squares using Knight moves, this was not done sequentially - i.e., the resulting magic squares (illustrated in the article) do not themselves demonstrate the Knight's Tour sequence and they cannot, therefore, be checked for accuracy of moves after completion. Compare that with the Ultimate Magic Tour example below. In my example, you can trace the sequence of every move 1-2-3 etc.

Also, UMT needs no memory work or calculation.

I haven't seen your own method, so I don't know whether that results in sequential Knight's Tour values. I assume it needs memory work.

BTW, although it usually makes sense to start numbering at "1", I do describe in UMT how you can start the sequence from any value (which can be freely chosen by the spectator).


Mike

Click here to view attached image.

My apologies to Hans-Christian. I completely forgot about his German ebook on his Magic Tour, "Magisch Vierkant 4", which you can find here https://www.lybrary.com/magisch-vierkant-4-p-926684.html

The biggest difference in these two approaches is that Hans-Christian's version requires a brilliant mind like his, meaning good memorization skills and a sharp mind during performance, while Michael's method doesn't require memorization as long as you do not perform it blindfolded.

Chris and Michael, thank you so much!
I'm curious about Michael's brilliant book.

My book features a Fully Magical Knight's Tour in which the audience specifies the starting board and the starting value. I know, a Fully Magical Knight's Tour seems impossible, but we are mathemagicians. My method is based on memory work, unlike Michael's method.
I'll also be very interested in comparing our two approaches.

I also developed another Fully Magical Knight's Tour, which, IMHO, is much more clever and inscrutable. But I don't want to release it just yet.
It's nice to know that we're not the only nerds into such obscure topics.

Many thanks to Hans-Christian, who has very kindly sent me a copy of his German ebook on the fully magic tour.

Having had the chance to study this fascinating work, I agree with Chris' assessment. I would add, however, that our two methods and overall approaches to the problem are also very different.

Hans-Christian has focussed on achieving the seemingly (and actually) impossible - creating a fully magic tour on an 8x8 board in which both diagonals also sum to the magic constant. Because this is impossible, his very clever (but challenging) solution inevitably involves a few sacrifices to the Knight's Tour procedure.

In contrast, UMT sacrifices the diagonals in the interests of maintaining the integrity of the Knight's Tour numerical sequencing. Technically, UMT produces a "semi-magic" square in which the two diagonals do not each sum to the magic constant. However, the sum of the two diagonals does equal twice the magic constant.

Mike