OK, so it took a little longer than expected, and we even had to go find a step stool, but as you can see (above) we eventually finished the tower :-)

Astute puzzlers noted that the sentence that began “Initially, “, and which then proceeded to sound like chatbot slurry, was itself a major clue. The initial letters from the words that followed spell out “n to the n equals a to the b”.

And so: the n^th level of the tower displays the number of ways to rewrite nⁿ in the form a^b, where a and b can be positive or negative integers. (As alluded to in the third paragraph.)

The least integer n for which nⁿ permits exactly 2023 such re-writings is 2² × 3¹⁶ × 5¹⁶ = 26,273,633,422,851,562,500.

The casework involved in solving for the least such n is fairly interesting; we’d love to share it but we’ve just been told we need to disassemble the tower tout suite to clear away table space for the research team’s daily game of Campaign for North Africa. Gotta go!

Congrats to this month’s solvers!