Kudos built on university logic puzzle (6)
I believe the answer is:
sudoku
'logic puzzle' is the definition.
'sudoku' can be an answer for 'puzzle' (I've seen this before). I'm unsure of the 'logic' bit.
'kudos built on university' is the wordplay.
'built' indicates anagramming the letters.
'on' means one lot of letters goes inside another (as in clothing \'on\' a person).
'university' becomes 'u'.
'kudos' is an anagram of 'sdoku'.
'sdoku' going around 'u' is 'SUDOKU'.
(Other definitions for sudoku that I've seen before include "filling boxes" , "Numbers game" , "Number game" , "Numerical puzzle" , "Numeric puzzle" .)