Actually, this magician's trick is "old" only in the sense that I worked it out some three decades ago; to my knowledge, it has never been used or published by anyone before now. This is a puzzle with no linguistic elements, but it may nonetheless be of some interest to palindrome-aware Word Ways readers.
"The Old Palindromical Equations Trick,"
Word Ways: Vol. 49
, Article 15.
Available at: https://digitalcommons.butler.edu/wordways/vol49/iss2/15