wangqh2696122 He was puzzled by this phenomenon. He began to try every approach known to find the best way of working it out. He began to try every known approach to finding the best way of working it out.
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wangqh2696122He was puzzled by this phenomenon.But those two sentences are quite odd and too wordy. I would say 'He began to try every known way
He began to try every approach known to find the best way of working it out.
He began to try every known approach to finding the best way of working it out.
wangqh2696122I cannot decide on find or finding. Could you please help me?He was puzzled by this phenomenon. He began to try every approach known to find/finding the best way of working it out.If you want to use your sentence, you should use 'find'.