Java Programming

hi there..
lately i've been studying dinamyc programming in java.
i found some interesting problem when i was chatting with my mentor

it goes like this..

each word is a multipolindrome, it mean that each word contain atleast 1 polindrome (if the word is a polindrome) or made from several polindrome (2 to n word that create the word)

for example, minimum is made from atleast 2 polindrome "minim" and "um" and max 7 polindrome (a single letter is a polindrome)

now teh question is how to make a program to calculate the minimum polindrom a an inputed string

i've been thinking of a way to make a subset from the string and use the dynamic programming approach to check from subset that contain i char where i is 1 to n char that make the input string

but i'm kinda stuck on how to do that.
thankz for the help