# Shortest path from one $\to$ ten with a twist - Updated

NOTE: The rules have been updated to cause the nature of the puzzle to be as intended. I will upvote the answer which was given before the change, but I look for both alphabetic and math operations to be used to solve the puzzle.

There are the kinds of puzzles where you take a number and try through math to get it to another number, or start with letters, and try to get to another word through a series of valid words... but what about a combination of the two.

The rules:

                           (15 14  5)
Starting with the letters: _ o  n  e_


and changing only one letter at a time or converting the letters to numbers, apply one mathematical operation specified below, you must follow the path of:

one $\to$ two $\to$ three $\to$ four $\to$ five $\to$ six $\to$ seven $\to$ eight $\to$ nine $\to$ ten

Each result of a letter substitution must be a valid English word. When converting to numbers, the results of the math do not need to be valid words when applying operations, but must be to switch back to letters (which must happen for each of the goalpoints).

Valid math operations: (all except rotation of numbers to a single characters digits)

$+1$,$-1$,$\times2$,$\mod27$,sum the digits (14 $\to$ 5),multiply the digits (14 $\to$ 4) rotate numbers clockwise or counterclockwise (15, 14, 5 $\to$ 14, 5, 15 etc)

Valid alphabetic operations:

add a letter, remove a letter, rotate characters clockwise or counterclockwise.

I will allow for roughly a month if there is interest and will accept the shortest path as the answer, with upvotes for partial solutions. Good luck!

Note: The switching of characters between numbers and letters does NOT count as a step, so does not penalize you.

• The rotation of numbers cannot be "to a single character's digits". – Jonathan Allan Jun 10 '17 at 21:31
• ...so are the others applied to each and every character or to a single one of our choosing (or either)? – Jonathan Allan Jun 10 '17 at 21:32
• Doesn't the "change a single letter" operation make all of the maths operations redundant? (as well as the rot13 single letter) – Jaap Scherphuis Jun 10 '17 at 21:33
• @JaapScherphuis Yep, I think the minimum path currently is dictated by Levenshtein distance. Edit: except words must me in a dictionary... – Jonathan Allan Jun 10 '17 at 21:37
• Updated wording to clarify what I meant by "step"... I meant each of one,two,three etc. – ben-Nabiy Derush Jun 11 '17 at 13:32