水火不容
Meaning
Two things or people that are fundamentally incompatible.
In a sentence
Those two departments are 水火不容.
Usage note
Stronger than "they disagree" — it implies irreconcilable opposition.
Where you see it in Brain Challenge
This idiom appears in the picture-idiom levels as a picture or number clue. When the clue shows numbers, the digits usually become the first characters of each half of the idiom — that is why so many chengyu start with 一, 三, 五, 七, 九 or 十.