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I am looking for an idiom or phrase that means "thinking hard by myself to solve a problem". I hope the idiom or phrase has the word "head" in it.

Example: I have been ____ head ______ for the last 5 days to solve this math puzzle.

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    You've been head down for the last 5 days, working on your problem. (You haven't even had time to look up at the rest of the world.)
    – Drew
    Commented Feb 20, 2017 at 4:19
  • "have one's head screwed on right : to have good judgment"
    – mahmud k pukayoor
    Commented Feb 20, 2017 at 4:25
  • 4
    This is what we call a "guessing game" question. They're not a good fit for the site. (more)
    – MetaEd
    Commented Feb 20, 2017 at 20:57
  • In case your answer doesn't really need the word "head" in it (I assume this is a homework assignment), you could also use "brainstorming". I think "head down" is the right answer for the homework though. :)
    – Christian Shay
    Commented Feb 21, 2017 at 13:32
  • My first thought to fill in the first gap with "giving". Then i realized... :D
    – Viktor Mellgren
    Commented Feb 22, 2017 at 11:58

11 Answers 11

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I have been scratching my head for the last 5 days to solve this math puzzle.

The Cambridge Dictionary says the following with regard to British English:

scratch your head

  • to think hard about something
  • A lot of people must be scratching their heads about which way to vote.

It also says the following with regard to American English:

scratch your head

  • to have difficulty understanding something
  • All I can do is scratch my head and ask why.

(link)

To address the point that you want something that means "thinking hard" instead of "to have difficulty understanding," I can attest as a native speaker of English in the United States that to scratch one's head does imply effort being put into solving a problem. Also, if someone is spending 5 days on a math puzzle they must find it difficult, the implication is present that some effort is being put into solving it is there anyway.

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    Welcome to English Language & Usage! We're looking for long answers that provide some explanation and context. Please explain why your answer is right, ideally with citations. Answers that don't include explanations may be removed.
    – NVZ ♦
    Commented Feb 20, 2017 at 6:24
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    Someone please find the courage to improve this answer because the suggestion's a good one ;)
    – Pierre Arlaud
    Commented Feb 20, 2017 at 9:28
  • Interesting, I'm from the US as well and when I say "I'm scratching my head" it means someone did something stupid and I don't get it, but also don't care. As in "the way you're standing in the rain has me scratching my head".
    – Carl
    Commented Feb 20, 2017 at 15:34
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    As a US speaker, "scratching my head" does not imply thinking hard to me. I'd understand it, but I'd think it's an odd usage of that expression. To me "banging my head against the wall" would be more reflective of thinking hard to solve a difficult problem.
    – Daniel
    Commented Feb 20, 2017 at 16:23
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    I think this is as close as it gets within the given constraints, although I agree with Carl and Daniel that "scratching my head" strongly suggests confusion rather than being deep in thought. racking one's brains has the desired meaning.
    – trent
    Commented Feb 20, 2017 at 23:14
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You have been trying to wrap your head around it.

The Free Dictionary says:

wrap (one's) head around

To comprehend something that one considers challenging, confusing, or a foreign concept.

So your sentence could be modified a bit:

I have been trying to wrap my head around this math puzzle for the last 5 days.

EDIT: As per Mari-Lou A's comment, in British English you can also say that you can't get your head around it.

From the Cambridge Dictionary:

If you say that you can't get your head around something, you mean that you cannot understand it:

I just can't get my head around these tax forms.

So the sentence would be:

I haven't been able to get my head around this math puzzle for the last 5 days.

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    I like this one the best
    – jumps4fun
    Commented Feb 20, 2017 at 14:04
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    very similar idea, apparently British English, but I'd say any Anglophone speaker would understand it, can't get your head around sth If you want, you can also add this suggestion.
    – Mari-Lou A
    Commented Feb 20, 2017 at 20:35
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    I'd say this phrase is entirely about understanding, as opposed to solving.
    – Rycochet
    Commented Feb 22, 2017 at 9:58
  • @Rycochet - the question was about thinking hard, so I think this phrase is appropriate here
    – Darkest of Nights
    Commented Feb 22, 2017 at 10:03
  • Wrapping your head around something means you got it. Doesn't mean you are trying to get it.
    – Lightness Races in Orbit
    Commented Feb 22, 2017 at 10:39
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You've been banging your head against a wall.

The Free Dictionary gives an example that is almost the same as your sample sentence.

To attempt continuously and fruitlessly to accomplish some task or achieve some goal that is or seems ultimately hopeless.

  • I feel like I've been banging my head against a wall trying to understand this math equation.
  • Some people are never going to agree with you on this, so it's no use banging your head against a wall trying to convince everyone.

Of course if you actually solved the problem, and did it in a clever way, someone might tell you that you really used your head (there).

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    I would say that "banging one's head" implies a fruitless and stressful experience.
    – GeoffAtkins
    Commented Feb 20, 2017 at 9:01
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    @GeoffAtkins That could be exactly what OP is looking for.
    – Spencer
    Commented Feb 20, 2017 at 11:58
  • I have heard people use "banging my head against <X>" where X may be something like "that bug" or specifically "bug 1234". I have seen it used such that the implication would be that sooner or later, either the bug or the speaker's head is going to break.
    – stannius
    Commented Feb 20, 2017 at 23:39
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There's racking my brain, which means exactly that and sort of comes close to an expression with "head" in it.

http://dictionary.cambridge.org/us/dictionary/english/rack-your-brains

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    In my experience "racking my brain" is only used when trying to remember something, not in trying to understand something.
    – AndyT
    Commented Feb 20, 2017 at 11:56
  • @AndyT, I don't know; I'm getting to the point where I rack my brains to figure out how to tie my shoes. :-)
    – fixer1234
    Commented Feb 20, 2017 at 11:59
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I've been doing my head in trying to come up with an answer.

Or less clumsily,

This maths question has been doing my head in for the last five days.

http://dictionary.cambridge.org/dictionary/english/do-sb-s-head-in

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    Isn't this just a more recent version of "banging my head against a wall", or is the etymology different somehow?
    – fenix d.Anconia
    Commented Feb 21, 2017 at 19:39
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If you're working with someone else, you can put your heads together to find a solution.

http://dictionary.cambridge.org/dictionary/english/put-their-heads-together

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You can "use your head" to solve a problem. Generally that implies thinking harder (or smarter) than you generally might do, in order to come to the correct answer/conclusion by yourself.

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    Often found in the form "Now that's using your head!" to praise someone for good thinking.
    – barbecue
    Commented Feb 22, 2017 at 18:13
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The term "headwork" comes to mind:

https://www.merriam-webster.com/dictionary/headwork

It would need to need some (head)work to fit in your sentence, however. Perhaps "doing some serious headwork." The verb form "headworking" doesn't appear in MW, or other sources I've found.

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To break or bust your head on a problem means to think really hard about it. I can't find it in online dictionaries but Google comes up with many examples.

David Bowie's Moonage Daydream has the variant I'm busting up my brains for the words.

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0

Just thinking about that problem "makes my head explode".

This has the connotation of extreme frustration while trying to understand or solve a problem. It is the logical consequence of "banging my head against the wall".

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Jerome Rodale, The Synonym Finder (1978) suggests trouble one's head.

Christine Ammer, The American Heritage Dictionary of Idioms, second edition (2013) offers this entry for the phrase:

trouble one's head with Also trouble oneself about. Bother or worry about, as in Don't trouble your head with these details; I'll take care of it, or It seems to me that teachers should trouble themselves more about teaching and less about manners. The first term dates from the mid-1600s, the variant from the early 1500s.

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