Alphamagic Square

A Magic Square for which the number of letters in the word for each number generates another Magic Square. This definition depends, of course, on the language being used. In English, for example,

$\begin{displaymath} \matrix{\hfil 5 & 22 & 18\cr 28 & 15 & \hfil 2\cr 12 & \hfil... ...fil 8\cr 11 & \hfil 7 & \hfil 3\cr \hfil 6 & \hfil 5 & 10\cr}, \end{displaymath}$

where the Magic Square on the right corresponds to the number of letters in

$\begin{displaymath} \matrix{\rm five & \hbox{twenty-two} & \rm eighteen\cr \hbox... ...& \rm two\cr \rm twelve & \rm eight & \hbox{twenty-five}\cr}. \end{displaymath}$

References

Sallows, L. C. F. ``Alphamagic Squares.'' Abacus 4, 28-45, 1986.

Sallows, L. C. F. ``Alphamagic Squares. 2.'' Abacus 4, 20-29 and 43, 1987.

Sallows, L. C. F. ``Alpha Magic Squares.'' In The Lighter Side of Mathematics (Ed. R. K. Guy and R. E. Woodrow). Washington, DC: Math. Assoc. Amer., 1994.