# Coded words of an old mobile keypad

Consider an old mobile keypad which looks like this.

The words produced according to the codes typed on the keypad are as follows:

Code Word
1* 17* 2* BACK
1* 145* 4* HIGH
0# 3568# 3# DEFT
0# 3569# 6# MOWN
1* 145* 2*
0# 23689# 3#

Which two words complete the table?

The two words that complete the table are:

BACH and DEFY

First note a consistency across all of the words provided - they comprise:

all three letters from a particular keypad key along with one other letter.

These are encoded within the pattern of each word:

The third part indicates the key number on which the three shared-key letters can all be found.

Meanwhile, the second part indicates the other letter to include, if you consider each of the numbers in this centre-part to be the position of a Braille dot when overlaid on the keypad.

NB The use of asterisk and octothorpe symbols between each part indicates whether our Braille grid uses the left two columns (asterisk) or the right two columns (octothorpe).

Finally, the first part of each code indicates:

which of the three shared-key letters begins the encoded word, where this number is the index of the letters on that key, with the first letter being represented by '0' (and thus the second by '1' and the third by '2').

We can show this for the given words:

1* 17* 2* = BACK
- Third part: Use the three letters from key 2, i.e. ABC.
- Second part: The additional letter is represented in Braille by dots on the 1 and 7, i.e. the letter 'K'.
- First part: The first letter of the word is the second one on the key, i.e. 'B'.
The only common word able to be spelled according to these conditions is BACK.

1* 145* 4* = HIGH
The letters from key 4 (GHI), with Braille letter H, with the second letter (H) appearing first.

0# 3568# 3# = DEFT
The letters from key 3 (DEF), with Braille letter T, with the first letter (D) appearing first.

0# 3569# 6# = MOWN
The letters from key 6 (MNO), with Braille letter W, with the first letter (M) appearing first.

Repeating this for the last two patterns gives us:

1* 145* 2* = BACH (the composer)
The letters from key 2 (ABC), with Braille letter H, with the second letter (B) appearing first.

0# 23689# 3# = DEFY
The letters from key 3 (DEF), with Braille letter Y, with the first letter (D) appearing first.

Finding patterns and considering that each could correspond to any letter of a group of 3 or 4, as shown on the phone, I came up with ihgk and pdyu.

They are listed as words here: https://www.thefreedictionary.com/words-that-start-with-pdy

But they don't look like words, so I'm not sure.