(This is part of an answer to Puzzle: Phone Numbers.)

You can encode a 4-letter name if you rearrange the keypad like this:

1 2 3 abc def ghi 4 5 6 jkl mno pqr 7 8 9 stu vwx yz * 0 #

That allows you to encode 4 letters:

ADRI = [(1,2,1), (8,3,6)]where the first number of each tuple is the rank of the combined indices of the other numbers:

1: 00 2: 01 3: 02 3: 10 4: 11 5: 12 6: 20 7: 21 8: 22

And this leaves you a few bits to play with, since you're only using 6 of the 7 digits of the telephone number. So why not use the last digit to encode an emoticon? You can have several vanity numbers, each ending with one of the 10 standard human emotions:

0: :) happy 1: :} extra happy 2: ;) sarcastically happy 3: :] squarely happy 4: :> avian 5: :| anhedonic 6: :\ mildly displeased 7: :P disgusted and/or gloating 8: :@ internet unhappy 9: :( unhappy

For example:

If she's feeling happy, Adriana gives you her happy number:

617-121-8360 = [(1,2,1), (8,3,6), 0] = ADRI:)

If she's feeling mildly displeased with you, then you get 617-121-8366.

But here's the real challenge. Is it possible to do better? It certainly seems impossible to uniquely encode a full 7-letter name like ADRIANA. There just aren't enough numbers on the keypad. But can you uniquely encode a 5-letter name like ADRIA?