Inspired by the common binary search algorithm, this design would be a binary or tertiary search on the next desired letter. Below are three potential visualizations of this, where a user would use the left or right arrow keys to narrow in on the desired letter. All three diagrams show the same progression of selection an “N”.
Binary Search Letter Selection Tree
Initially Billy is given two options "A-M" or "N-Z". By hitting the "right arrow", two nodes appear under "N-Z" further dividing the letters into "N-T" or "U-Z". This could continue until Billy ends up at only one letter, which would require 4-5 key presses. The design shown above narrows down to three letter, at which point Billy could use the "left", "right", "select" keys to choose from one of three possible letters.
Binary Search Letter Selection List
Although the tree display above is very compact, it might be mentally cumbersome to determine where in the alphabet a letter exists. The design below also utilizes binary search but shows Billy all the possible letters he is choosing from. By select left or right, n/2 remaining possibilities are highlighted, and he then uses the "select" button to narrow in.