In this problem you have to choose one of the two phrases in brackets.

You can find some way to enjoy math more. Think of each math problem as a puzzle (to solve / to be solved). Or look for math in everyday life.

I chose 'to solve', but the answer was 'to be solved'. I thought 'a puzzle to solve' is similar to 'a book to read' phrase. (You) think of each math problem as a puzzle (for you) to solve. Doesn't this sound more natural?

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    I wouldn't mark either answer as "wrong", with "to be solved" maybe being a bit more natural to my ears, but I'm not even sure why. Feb 20, 2020 at 15:21
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    Then you might think that both can be correct?
    – Andrew
    Feb 20, 2020 at 15:36
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    It's a stupid "test". Both forms are perfectly grammatical, and in almost all contexts they're effectively interchangeable. At the absolute margins, one could contrive a context where the to be solved version implied ...by someone else, whereas the to solve version would probably always imply ...by you (the addressee). Feb 20, 2020 at 16:21
  • The only real difference is that the "to be solved" form is passive. The problem waits there for somebody to solve it. The "to solve" form is active. The person is going to go do the solving.
    – puppetsock
    Feb 20, 2020 at 17:55

1 Answer 1


Both are correct and idiomatic.

The verb "solve" normally has the person as the subject and the puzzle as the object

I solve the puzzle. / The puzzle is solved (by me)

However in infinitive phrases, the object can seem to precede the verb. Consider

"a cake to eat"

or with a bit more context

I want a book to read while I'm on holiday.

In these cases the infinitive phrase modifies or describes the word "cake" or "book" (by giving its purpose) In such infinitive phrases the you can omit the subject and the object (it is inferred from the context that the subject is "I" and the object is "book".)

As such, the passive and active voice in this kind of infinitive phrase mean the same.

a cake to eat == a cake to be eaten (by someone)

But if you want to be specific about the subject, you need the passive, so you can give a "by" phrase.

I want a book to be read by my daughter.

In your case, the use of the passive implies the existence of a solver (which is you in the context) This is probably why "to be solved" is a good answer. Compare this with ergative verbs "The door opened/The door was opened". However, both are possible in the given context.

  • Thanks to everyone!
    – Andrew
    Feb 20, 2020 at 16:58

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