Learn English – “Reasons for…” or “Reasons that…”

"Could" is an auxiliary verb with multiple uses. "Could you get me a glass of water?" (asking someone to do something) "He could grow up to be President" (expressing possibility) "He could not climb the tree." (expressing ability or inability) There may be other uses, as well. Considering the third example, though, it shows that there is nothing wrong with saying ""I could only answer half the questions" to mean "I was only able to answer half of the questions." The only difference is that (in the absence of the first sentence, which sets the time in the past) the former version is subject to the possible interpretation "It is possible that I will decide to only answer half of the questions."

Note that I have said "half of the questions." English usage requires the definite article in this case.

The coach said that they _________ to the gym every day next week to get in shape for the tournament game.

1) should go
2) will go
3) will be going

Any of the three options work. The sentence is reported speech. The reported speech includes the phrase "next week", which–when used properly–refers to a situation that has still not happened at the time of the reported speech. Since this is the case, the modal verb will is fine; it can, but does not have to, be backshifted (to would) in this case. Thus, both 2 and 3 are okay. 1 is also okay in this context.

If, on the other hand, the time meant by "next week" is already over when the sentence was said, then the phrase "next week" should have been changed to "the following week" and any present tense verbs, including modals, backshifted to the past tense. In this case, will would become would in both 2 and 3. Should would still work, because it cannot be backshifted.