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crux (noun) the essential point (of a problem, matter, question, or issue).
The most important or difficult stage in our attempt to solve a problem is the crux of the problem. The crux of the matter is the essential part of the matter. In other words, the crucial stage in a problem is its crux. 'In whose favor the chairperson will cast her vote is the crux of the problem.' This means that the chairperson's casting vote is going to be important and will decide who will win. The crux of the burning issue of world peace is whether the nuclear powers will agree to a total disarmament. That is, if the world's nuclear powers agree to a total disarmament, world peace is possible.
- 'Will it rain, or won't it?' This is the crux of the problem, as the crops here are totally dependant on rain, and the prospects of a good harvest are tied up with good rains.
- The crux of the matter is, whether the three like-minded parties will form an alliance or not, as no single party has emerged with big enough majority to form the government.