Inspired by the common binary search algorithm, this design would be a binary or tertiary search on the next desired letter. Below are twopotential 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. After a letter is selected, the visualization returns to the root node.
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.
For both designs the following would be necessary
Spaces - Hitting the down key would insert a space
Punctuation/numbers - Numbers could be added. The first choice could be ("A-M" OR "N-Z, 1-9") or ("Letters" OR "Numbers"). Punctuation would be hard to accomplish in the tree representation, as punctuation as has no ordering, unlike the alphabet. Punctuation could work well in the list representation though, by simply appending punctuation after "z".
Safety
If in the middle of selecting a letter, a wrong choice is made, Billy could simply hit the "up" key which would move back up a level in the tree. If an entirely wrong letter is input, again hitting the up key from the root node could delete a previous letter.
Learnability
The tree representation might be confusing to understand, but we believe it would be fairly obvious to pick up (assuming Billy knows the order of the alphabet). Deleting an entered letter or moving up a level in the tree also seems fairly intuitive, but will need to be tested.
Efficiency
If Billy is required to halve until one letter remains, this would take 4-5 selections. It might be more efficient to make two cuts so three letters remain, and let Billy choose from one of the three. People who play video games often remember short key sequences as combination moves in games, and might be quick to remember the key presses for word combinations.