Open problem: optimal calculator keyboard layout based on key usage statistics

[ttw]

I don't know about calculators, but in typing, the backspace seems to be the most common key (not counting the alphabet and spacebar.)

Digit key frequencies do not follow Benford's Law as that only applies to the first digit. This doesn't matter too much as either calculator order (as you suggest) or the phone order are about the only two that need no thought from the user.

Making "Enter" double sized is good. Another thing I would like is to have separate "Backspace" and "Delete" keys. I find that during editing (words or numbers or codes) I often end up wanting to delete the character under the cursor about as often as that preceding the cursor. If wrong, most calculators take two keystrokes, either a shift key and the Delete (or Backspace) or an arrow key to move to the position that needs no shift.

The HP 48, 49, 50 series seems to get some advantage by having the function keys operate from a menu that one can program. I use this often to assign either programs or things that take lots of keystrokes to find to my custom menus. Working with big integers uses things like Mod and Divide with Remainder but working with reals uses other things like Round or Truncate, etc., for example.