Hi Kooyeen, One way of explaining differences between to-infinitive and -ing is: verb + ing = for actions already regularly experienced (or being experienced in an ongoing way) and/or familiar to + infinitive = less familiar/regular or hypothetical So for your first pair of sentences, the first one sounds like a problem that is hypothetical, in the future or part of a plan, while the second one sounds like this has been a problem already experienced or ongoing at the time of speaking. The theory generally works for your second set as well. For the first set, I don't think I would ever say "was to touch" - but I might use it in a future sense (it will be weird to touch that big gravestone).
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EnglishRavenSo for your first pair of sentences, the first one sounds like a problem that is hypothetical, in the future or part of a plan, while the second one sounds like this has been a problem already experienced or ongoing at the time of speaking. The theory generally works for your second set as well. For the first set, I don't think I would ever say "was to touch"