It is a problem which has only one solution. For example, the square root of 4 has two solutions: -2 and +2. However, if the question is presented in the context of the length of a side of a square whose area is 4 units, then there can be only one answer: +2. There cannot be a negative length.
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Depends on the type of math problem. there's usually an equation to see if there is a solution or not.
A problem and a solution are not synonyms or antonyms, but rather concepts that are related. A problem is a challenge or difficulty that needs to be solved, while a solution is the resolution or answer to that problem. They are not homophones, as they do not sound alike.
By definition, you cannot. To solve means to find an answer or solution to a problem or a question. If there is no solution you cannot find one.
You gain relevant insights from solving that one problem, and then you can use those insights to help guide you to the solution of the original problem.
It depends on the problem but the solution is always the answer.