# From bottom to top

A twist on the word-ladder type of puzzle:

Reach from "bottom" to "top", following these rules at each step:

1. You can change a letter, remove a letter or add a letter at each move.
2. The changed letter can change its place in the word. For example, if I want to change the second "e" in the word "there", I can change it to "i" and move it before the "r" of the word to make the word "their".
3. No other letters in the word can change their order (unless you reverse their order). For example, "order" can be changed into "redo" in one step by removing the second letter and reversing the order of the others. However, you cannot change it into "rodeo" in one step, as it would require changing the order of the letters.

PS. To avoid controversial issues regarding whether something is a word or is not a word, the word must appear in the uncensored Mammoth word list on Litscape.

Neither "mott", nor "moto" appear in this list. Proper names are not allowed.

3 Intermediate Steps

bottom
motto (drop "b" and reverse)
potto ("m" to "p")
pott (drop "o")
top (drop "t" and reverse)

Solution 1. - 3 intermediate steps.

bottom
motto (removed b and reverse word)
mott (remove o from the end)
tom (remove last t and reverse word)
top (replace m with p).

Solution 2 (because people complain about the word mott, I don't know why :D) - 5 intermediate steps

bottom
motto (removed b and reverse word)
motor (replace a t with an r and move the r to the end)
room (remove t and reverse the word)
root (replace m with t)
too (remove r and reverse order)
top (replace last o with p)

• Found that too, but Mott is a name… not counting dialects. Mar 22, 2017 at 8:49
• @JanIvan: urbandictionary.com/define.php?term=mott . Mar 22, 2017 at 9:00
• Since solution 1 is a bit controversial - whether or not "mott" is a valid word, I would count your solution 2. And the funny thing is - that is what I found when solving the puzzle myself. Still, would give the people a chance to find a better one (or you). :) And would wait a bit before accepting an answer. Mar 22, 2017 at 9:05
• @Marius In urban "dictionary" you can find definition for anything urbandictionary.com/define.php?term=qwertyuiopasdfghjklzxcvbnm Mar 22, 2017 at 9:29

I hope I understood the rules

bottom
motto $\rightarrow$ remove b and reverse
motor $\rightarrow$ replace t with r and place at the end
room $\rightarrow$ remove t and reverse
moo $\rightarrow$ remove r and reverse
mop $\rightarrow$ replace o
top $\rightarrow$ replace m

I'm assuming we can't use a proper names.

• Your solution is practically a tie with the one Marius did. But since he presented his solution (the second, valid version) first, I accepted his answer. For now. :) Unless someone beats it with less steps in the future. Mar 22, 2017 at 15:19
• @MariaDeleva No problems :-) Mar 22, 2017 at 15:19

## 4 steps -

bottom

1. motto   (remove b and reverse)
2. moto   (remove t)
3. tom   (remove o and reverse)
4. ...   (replace m with p)

top

• I have updated my question - to avoid "controversial words". Mar 22, 2017 at 9:45

4 Intermediate steps:

bottom
motto (drop "b" and reverse)
motor ("t" to "r" and move)
roto (drop "m" and reverse)
rot (drop "o")
top ("r" to "p" and reverse)

• Is "roto" a word? Mar 22, 2017 at 16:29
• @randal'thor It does appear on the list of words in Litscape. So it is valid. It says it is short for "rotogravure". Mar 22, 2017 at 18:35

# 3 intermediate steps

bottom -> motto -> moot -> too -> top

• I guess motto -> moot is not valid. Mar 22, 2017 at 12:02
• @Techidiot is correct. Mar 22, 2017 at 12:07

I hope I understood it right.

## 2 intermediate steps -

bottom

1. botte   (remove m and change second o to e)
2. boat   (remove t, change e to a and move to between o and t)
3. top   (reverse, remove a and change b to p)

top

• I believe your operations are too complex. You can't remove a letter and change another letter in a single step. ("You can change a letter, remove a letter, or add a letter at each move": emphasis added.) Mar 22, 2017 at 21:24
• What @Hellion said is correct you can only do one letter change at each move - regardless of whether you remove it, add it or replace it with another letter. If you replace it with another letter, or add an letter - you can place it anywhere in the word. But the order of the other letters should remain the same, or they should be in reverse order. Mar 22, 2017 at 21:33