Usage of "a" and "the"

Question

 I have a question related to usage of a and the following sentence. Can anyone please tell me which one sounds better in in the following sentence?

• For some days, street dogs have bitten more than 20 people in our locality. people are afraid of getting out of their houses. It's a big problem. We have to find a/the solution to the problem.

I think both are correct. In general, there sometimes is only one solution to a particular problem so I think I can use the. Sometimes the situation gets such grave that it is hard to find a solution and we start thinking if there is any solution to the problem. In that situation, can I use the? And sometimes, there is more than one solution so I can use a. What's your opinion?

Can any person knowing the language well answer this please?

Answer 1

Some problems have a single unique solution, but others do not. If you know in advance that there is a single solution, then you can use the.

For example, if you were asked to solve an arithmetic problem (e.g. 12+13), then there will usually only be a single correct solution. In that case, you may be asked:

Find the solution to the following problem.

You cannot use 'a' to replace 'the' in this case, as this would imply that there is more than one correct solution.

In the situation described in your question, it is unlikely that their will be a single unique solution to the problem. More likely you will generate several potential solutions, from which you will select a solution that you will implement. It is also possible that you will implement more than one of the solutions that you generated. In cases such as this you cannot refer to the solution, you need to refer to a solution or to solutions. e.g.

We have to find a solution to the problem.

or

We have to find solutions to the problem.