Which written languages cannot have crossword puzzles due to limitations of their characters? ~

I've never seen a crossword in Chinese or other Oriental language. 

i think they can all have thenn

A crossword puzzle is theoretically possible in Japanese or Chinese, though they would be a bit limited. You would have to find words that contain the same characters, thus words that intersected would have to be thematically related and since most words don't contain more than a few characters, the puzzle would be very small unless entire phrases were used.

I'm not sure how a crossword puzzle would work in a Semitic language where vowels are often not marked in the script.