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I wonder which form(s) are correct amongst the following:

  • the challenge to do X
  • the challenge of doing X

Example:

The models in the literature tend to employ different strategies to encode the input, leading to the challenge to determine the best input encoding scheme for this problem.

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  • Good question, I think both are correct, however, I don't know why I have a feeling that "a challenge" sounds better than "the challenge" I have no idea to support. I would say "leading to a challenge to ...". I am a learner though. – Cardinal May 10 '19 at 5:25
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Both are grammatically fine. "the challenge to do X" emphasizes X as unit, a thing to be accomplished. "the challenge of doing X" emphasizes X as a process, perhaps with challenging aspects or steps. But in many contexts the meanings of the two forms will be essentially identical.

The example sentence:

... leading to the challenge to determine the best input encoding scheme ...

could be rewritten as

leading to the challenge of determining the best input encoding scheme ...

with no significant change in meaning.

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