The Pony and the Cart

[Taken from Mensa p. 69 with rephrasing by John Palinski and Sam Rebelsky.]

Farmer Johnson always has trouble connecting his pony to the cart. The residents of the island decided to help him by designing a problem that would help him lead the pony to the cart. They wrote the words PONY and CART in a column with some space between them and said

You can lead your pony to the cart by changing one letter at a time and keeping the remaining letters in the same spot. Each time, you'll arrive at a new word. Eventually, you should be able to get from pony to cart.

Here's the picture they drew, Can you use it to help Farmer Johnson?

 P   O   N   Y

___ ___ ___ ___

___ ___ ___ ___

___ ___ ___ ___

___ ___ ___ ___

___ ___ ___ ___

 C   A   R   T

Stuck? Try working from the bottom.

Explain your strategy for answering this problem. Where did you begin?