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I would like to get a clarification whether I do understand and use those two phrases correctly or not.

The context is solving a mathematical problem.

  1. solved with sth - means a problem is tackled using sth method
  2. solved for sth - means that a problem is transformed in such way that can sth can be obtained directly (as in "solve for x")

My question is, am I missing any meanings, or confusing them?

I got confused with the following sentence: "This problem is hard to solve for some methods" which I believe is incorrect, as one should not solve problems to obtain methods but by using them. I tried looking on several online dictionaries to solve + preposition compounds, but I found nothing.

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    I think your hard to solve for probably represents hard for some methods to solve - that is, the for phrase modifies hard rather than solve. – StoneyB on hiatus Jun 11 '14 at 10:38
  • @StoneyB Yes, indeed, the intended meaning is as you describe it. I would like to know if this is correct usage, maybe the difference lies in punctuation. I got quite puzzled. One can of course derive the meaning from the context, but I would like it to be grammatically and syntactically correct. – luk32 Jun 11 '14 at 12:25
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    It is acceptable in spoken contexts, but should be avoided in written contexts, where the Rule is "Anything which can be misuderstood will be". Point as is hard to solve, for some methods, or shuffle as is hard for some methods to solve or is for some methods hard to solve. – StoneyB on hiatus Jun 11 '14 at 12:36
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I don't see anything wrong with "This problem is hard to solve for some methods". It's the same basic form as...

"It's difficult for many algorithms"

...where we assign a degree of animacy to the algorithm, enabling it to face (and either overcome, or be defeated by) difficulties.

Obviously the method, algorithm, approach doesn't normally have the autonomy to apply itself, so in practice there'll be a person (or at least something more "sentient" than a process) using it. But I personally would draw a slight distinction in these cases - if it's difficult for the method, perhaps it needs a lot of computer resources, or can't handle certain unusual combinations of input data. If it's difficult using the method, perhaps the researcher has to go to a lot of trouble to apply the method, or is often dissatisfied with the results.


OP is perfectly correct that solve for X means establish the value of X (using some method which is invariably part of the context (i.e. - X is an output). But solve with X (or using X) normally applies where X is a method (or feasibly an input value).

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