What is the smallest cardinal number that its standard constructed English name encompasses the most distinct letters of the English alphabet?
I will hazard a reply, but feel there must be better answers. If I understand the specs, we want to use as many letters (A..Z) as possible (given "standard constructed English name(s)" whatever that is) and then look for the numerically lowest cardinal number having that maximum letter count.
Using what I would regard as "standard" names, there are only three letters which do not occur (J, K, Z), though z might be brought in to read "zero" at some place -- though this names a digit, not a number we could use.
The first part seems fairly forced, because there are only six terms which use letters C,P,Q,B,M: oCtillion, sePtillion, Quadrillion, Billion, and Million so I would START with:
"One octillion, One septillion, One Quadrillion, One Billion, One Million" ... and finish with 2568 (which I would read as "Twenty five hundred, sixty-eight"). I was hoping to start this part with either "twelve hundred" or "eleven hundred", but couldn't find a way to use all 23 letters without getting a higher cardinal in the last six digits.
I'll post this, and see what others find -- and perhaps revisit those last four digits.