however · adverb /ˌhaʊˈev.ər/Full view
however
A2 used when you are about to say something which is surprising compared with what you have just said
Dictionary examples:

This is one possible solution to the problem. However, there are others.

There may, however, be other reasons that we don't know about.

Learner example:

I will be very happy to go fishing and swimming in the lake like the last time. However, if you don't want to do it, it's not a problem for me. (Key English Test; A2; French)

however cold/difficult/slowly, etc.
B2 used to say that it does not make any difference how cold/difficult/slowly, etc.
Dictionary examples:

We're not going to get there in time, however fast we drive.

However hungry I am, I never seem to be able to finish off a whole pizza.

If Emma likes something she'll buy it however much it costs.

I'll see you after the show and give you £20 for the tickets, or however much they cost.

Learner example:

We think that we are careful and that we can avoid traffic accidents, but however careful we may be, some other people might be careless and hit us. (First Certificate in English; B2; Japanese)

however · conjunction /ˌhaʊˈev.ər/
however
C2 in whatever way
Dictionary examples:

However you look at it, it's still a mess.

You can do it however you like, it really doesn't matter.

Learner example:

However you do it, the important part is that you relax. (Certificate of Proficiency in English; C2; Greek)

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