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?

Only 9 letters per row allows three number words, ONE, TWO and TEN, to be spelled with 12 or fewer presses.

Posted by K Sengupta on 2023-09-11 01:45:27