TiVo's and other DVR's, such as those provided by the Cable TV company, allow searches for programs using an on-screen alphabet that you can move through using up, down, left and right buttons so you can select a letter with the enter button, then go on to select the next letter, etc.

One such alphabetic layout is as follows:

ABCD
EFGH
IJKL
MNOP
QRST
UVWX
YZ

The cursor always starts at A before the first letter of the word is typed. There is no wrap-around, so you can't go from A to Y in one step, nor from X to U in one step, and you can't go down from W or X, or right from Z.

Typing THIRTY using the above layout requires 30 button presses: DDDDRRR=UUU=LLLD=DDR=RR=LLLDD=, here using the = to represent Enter, and initial letters to represent Up, Down, Left, Right.

Suppose a different DVR has a different number of letters in each row. Using that DVR, with more letters per row, the word LOW can be typed in 12 or fewer button presses. On this same DVR, there are three number words (such as EIGHT, EIGHTEEN or EIGHTY, but those are just examples, not the answer) which also require 12 or fewer button presses each.

How many letters are there on a line on this other DVR, and what are the three numbers that can be spelled with 12 or fewer button presses each?

The most likely solution is a layout in a 3 row by 9 column area, where the number of letters on each line is 9 with the middle line having one less (i.e., 8), and the three natural numbers, spelled out in 12 or less key presses, are each 3-letters in length.

ABCDEFGHI
JKLMNOPQ
RSTUVWXYZ

LOW : 10 : DRR=RRR=D=
ONE : 11 : DRRRRR=L=U=
TWO : 11 : DDRR=RRR=U=
TEN : 12 : DDRR=UURR=D=

Other numbers, i.e., mathematical constants, can also be spelled out in 12 or less key presses. Examples of which are: PI (Archemedes' constant), E (Napier's constant), and I (the imaginary unit). So may numbers spelled out in other languages, such as the Spanish 1 (UNO) and the Tongan 6 (ONO). And many Roman Numerals, which are represented by the same letters found in the standard English alphabet, such as for 3 (III), can also be entered in 12 or less key presses. Yet, the assumption I have made is that number in the puzzle's text refers solely to American English cardinal numbers, thus I omit these alternatives from the given solution.

The following layout of staggered length in a 4 row by 8 column area will also work:

ABCD
EFGHIJK
LMNOPQRS
TUVWXYZ

LOW :  9 : DD=RRR=D=
ONE : 12 : DDRRR=L=LLU=
TWO : 11 : DDRR=RRR=U=
TEN : 12 : DDD=RRR=U=

As each spelled out number requires two key presses for each letter, (assuming the letters in the spelling were adjacent but not repeated and does not begin with 'a'), the maximum length possible would be 6 characters. (As it is, few letters in most number spellings are adjacent and none begin with an 'a'.) The longest number I have found that could be spelled in 12 or less key presses, with the requirement that LOW is spelled with 12 or less key presses, is of length 5. Just examine the following layout of staggered length of a 6 row by 8 column area:

ABCDE
FGH
IJK
LMNOPQRS
TUVWX
YZ

LOW   : 10 : DDD=RRR=D=
TWO   : 11 : DDDD=RRR=U=
FIFTY : 12 : D=D=U=DDD=D=

Edited on September 15, 2008, 3:58 pm

Posted by Dej Mar on 2008-09-15 13:44:40